Stony Brook Mathematics
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► MAP 102/103: Proficiency Algebra
About this Course
Lecture 01: Numbers and Operations (
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Lecture 02: Numerical Expressions (
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Lecture 03: Variables and Algebraic Expressions (
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Lecture 04: Addition and Multiplication (
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Lecture 05: Subtraction and Division (
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Lecture 06: Distributivity (
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Lecture 07: Powers (
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Lecture 08: Power Rules (
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Lecture 09: Polynomials (
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Lecture 10: Operations with Polynomials (
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Lecture 11: Rational Expressions (
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Lecture 12: Operations with Rational Expressions (
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Lecture 13: Composing Algebraic Expressions (
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Lecture 14: Equalities, Identities and Equations (
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Lecture 15: Linear Equations (
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Lecture 16: Applications of Linear Equations (
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Lecture 17: Linear Inequalities (
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Lecture 18: Absolute Value (
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Lecture 19: Lines on a Plane. Part 1 (
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Lecture 20: Lines on a Plane. Part 2 (
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Lecture 21: Linear Systems. Part 1 (
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Lecture 22: Linear Systems. Part 2 (
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Lecture 23: Linear Systems. Part 3 (
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Lecture 24: Radicals (
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Lecture 25: Radicals as Powers with Rational Exponents (
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Lecture 26: Quadratic Equations (
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Lecture 27: Quadratic Formula (
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Lecture 28: Factoring Quadratic Polynomials (
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Lecture 29: Equations Reducible to Quadratic (
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Lecture 30: Parabolas (
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Lecture 31: Quadratic Inequalities (
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► MAT 122: Overview of Calculus
About this Course
Lecture 03
: Functions and Interval Notation (September 1, 2017) (
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Lecture 04
: Linear Functions (September 6, 2017) (
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Lecture 05
: Quadratics and Other Functions (September 8, 2017) (
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Lecture 06
: Mathematical Modeling (September 11, 2017) (
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Lecture 07
: Limits (September 13, 2017) (
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Lecture 08
: More Limits (September 15, 2017) (
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Lecture 09
: Still More Limits and Continuity (September 18, 2017) (
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Lecture 10
: The Definition of the Derivative (September 20, 2017) (
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Lecture 11
: More Definition of the Derivative (September 22, 2017) (
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Lecture 12
: The Power Rule (September 25, 2017) (
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Lecture 13
: Equation of Tangent Lines (September 25, 2017) (
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Lecture 15
: Review of Midterm 1 (October 2, 2017) (
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Lecture 17
: Going over the midterm (October 6, 2017) (
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Lecture 18
: The Product and Quotient Rules (October 9, 2017) (
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Lecture 19
: The Chain Rule (October 11, 2017) (
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Lecture 20
: Tangent Lines, Higher Derivatives, and Concavity (October 13, 2017) (
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Lecture 21
: Maxima and Minima (October 16, 2017) (
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Lecture 22
: Curve Sketching (October 18, 2017) (
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Lecture 23
: More Curve Sketching (October 20, 2017) (
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Lecture 24
: Curve sketching of difficult functions (October 23, 2017) (
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Lecture 25
: Exponentials and logarithms (October 25, 2017) (
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Lecture 26
: Midterm review, part 1 (October 27, 2017) (
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Lecture 27
: Midterm review, part 2 (October 30, 2017) (
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Lecture 28
: going over midterm 2 (November 1, 2017) (
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Lecture 29
: Antiderivatives (November 3, 2017) (
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Lecture 30
: More antiderivatives and word problems (November 6, 2017) (
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Lecture 32
: Riemann sums (November 10, 2017) (
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Lecture 33
: More Riemann sums (November 10, 2017) (
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Lecture 34
: The Fundamental Theorem of Calculus (November 15, 2017) (
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Lecture 35
: Average Value (November 17, 2017) (
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Lecture 37
: Integration (November 27, 2017) (
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Lecture 38
: Integration by substitution (November 29, 2017) (
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Lecture 39
: Substitution and Word Problems (December 01, 2017) (
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Lecture 40
: Final exam review, part 1 (December 04, 2017) (
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Lecture 41
: Final exam review, part 2 (December 06, 2017) (
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Lecture 42
: Final exam review, part 3 (December 08, 2017) (
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► MAT 123: Precalculus
About this Course
Definition of Sine and Cosine (in Right Triangles) (
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The SOH CAH TOA mnemonic (
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Lecture 01
: Introduction to Trigonometry (
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Trig values for special angles (
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Lecture 02
: Right-triangle Trigometry (
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The unit circle and trigonometry (
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Radian measure (
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Lecture 03
: Radian measure and trig on the unit circle (
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Lecture 04
: Simple trig identities (
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Lecture 05
: Other trig functions & graphs of sine and cosine (
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Graphs of sine and cosine (
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Function notation (
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Domain and range (
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Lecture 06
: Functions, domain and range (
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Composition of Functions (
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Lecture 07
: Composition of functions (
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Lecture 08
: Piecewise functions, graph transformations (
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Inverse Functions (
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Lecture 09
: more graph transforms, inverse functions (
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Lecture 10
b: Review for first midterm (
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Lecture 11
: More review (
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The Slope of a Line (
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Lecture 12
: Lines, circles, and parabolas (
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Rules of Exponents (
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Lecture 13
: Exponents, ellipses, polynomial division (
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Rational functions (
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Lecture 14
: Rational functions (
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What is a logarithm? (
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Rules for manipulating logarithms (
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Lecture 15
: Exponentials and logarithms (
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Lecture 16
: Compound interest, e, and the natural logarithm (
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Exponential growth and decay (
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Lecture 17
: Exponential growth/decay problems and logs (
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Lecture 18
: Review (logs & exponentials) (
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Lecture 19
: Review for midterm 2 (
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Lecture 20
: Trigonometry review, Law of Sines (
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Lecture 21
: Law of sines, law of cosines, inverse trig functions (
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Lecture 22
: Inverse trig functions (
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Lecture 23
: Angle sum, double angle, and half-angle formulae (
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Lecture 24
: More trig&inverse trig; basic graphs (
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Lecture 25
: A garden of graphs (
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Lecture 26
: Graphs and solving equations (
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Lecture 27
: more equation solving; review (
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Lecture 28
: more review (
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Final Review: (
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Midterm 1 Review: (
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► MAT 125: Calculus A
About this Course
Lecture 01
: Course info and precalculus review. January 28, 2015 (
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Introduction to Limits, pre-lecture (
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Definition of the Limit (optional material) (
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Lecture 02
: Tangents, velocity, and limits. February 4, 2015 (
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Lecture 03
: Limits, Limits involving infinity. February 9, 2015 (
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Definition of the Derivative, pre-lecture (
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Lecture 04
: Limits and Continuity. February 11, 2015 (
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Lecture 05
: Definition of the Derivative. February 16, 2015 (
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Lecture 06
: The function f'(x); what does f' say about f?. February 18, 2015 (
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Midterm I Review Session. February 22, 2015 (
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Lecture 07
: The power rule & some review. February 23, 2015 (
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Lecture 08
: Some more review. February 25, 2015 (
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The derivative of exponentials, pre-lecture (
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Lecture 09
: The product and quotient rules. March 2, 2015 (
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Lecture 10
: Derivatives of trigonmetric functions. March 4, 2015 (
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Intuitive explanation of the Chain Rule (
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Lecture 11
: The chain rule. March 9, 2015 (
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Lecture 12
: Implicit differentiation. March 11, 2015 (
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Lecture 13
: Derivative of logarithmic functions. March 23, 2015 (
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Lecture 14
: Derivative of inverse trig & logarithmic differentiation. March 25, 2015 (
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Midterm II Review Session. March 29, 2015 (
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Lecture 15
: Review for second midterm. March 30, 2015 (
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Lecture 16
: Linear approximations and differentials . April 1, 2015 (
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Lecture 17
: Related rates. April 6, 2015 (
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Lecture 18
: More related rates, local maxima/minima . April 8, 2015 (
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Lecture 19
: Max/min and curve sketching. April 13, 2015 (
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Lecture 20
: Derivatives and the shape of curves. April 15, 2015 (
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Lecture 21
: Optimization word problems (first 9 minutes of audio missing). April 20, 2015 (
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Lecture 22
: More optimization, some review. April 22, 2015 (
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Lecture 23
: l'Hopital's rule and Newton's method. April 27, 2015 (
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Lecture 24
: Antiderivatives. April 29, 2015 (
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Lecture 25
: some review for final. May 4, 2015 (
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Lecture 26
: more review. May 6, 2015 (
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Final Review Session . May 11, 2015 (
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► MAT 126: Calculus B
About this Course
Lecture 01
: Review of derivatives and basic antiderivatives. January 25, 2016 (
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)
Lecture 02
: Antiderivatives and Riemann Sums. January 27, 2016 (
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Lecture 03
: Riemann Sums. February 1, 2016 (
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Lecture 04
: Definite Integration. February 3, 2016 (
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Lecture 05
: The Fundamental Theorem of Calculus. February 10, 2016 (
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Lecture 06
: The Substitution Rule. February 15, 2016 (
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Lecture 07
: More Substitution and Midterm 1 Review. February 17, 2016 (
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Lecture 08
: Midterm 1 Review. February 22, 2016 (
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Lecture 09
: Integration by Parts. February 24, 2016 (
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Lecture 10
: More Integration by Parts and Trigonometric Integrals. February 29, 2016 (
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Lecture 11
a: Trig integrals. March 1, 2017 (
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Lecture 11
b: More trig integrals and trig substitutions. March 6, 2017 (
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Lecture 12
: Partial Fraction Decomposition. March 7, 2016 (
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Lecture 14
: Practicing Integration Techniques. March 21, 2016 (
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Lecture 15
: Improper Integrals. March 23, 2016 (
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Lecture 16
: Volumes of Revolution - Washers and Discs. March 28, 2016 (
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Lecture 17
: More Volumes of a Solid of Revolution, and Volumes with known cross-sections. March 30, 2016 (
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Lecture 18
: More review for Midterm 2 . April 4, 2016 (
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Lecture 20
: Midterm Exam 2 review. April 11, 2016 (
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Lecture 21
: Volume -- Cylindrical Shell Method. April 13, 2016 (
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Lecture 22
: Finding Arc Length. April 18, 2016 (
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Lecture 23
: Average Value of a Function. April 20, 2016 (
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Lecture 24
: Applications to Physics and Engineering. April 25, 2016 (
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Lecture 25
: Finding the hydrostatic force and pressure. April 27, 2016 (
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Lecture 26
: Review for the Final exam. May 2, 2016 (
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Lecture 27
: Final Exam Review - Part Two. May 4, 2016 (
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► MAT 127: Calculus C
About this Course
Lecture 00
: Course Introduction - What is MAT127 about? (
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Lecture 01
: Infinite Sequences (
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Lecture 02
: Convergence of sequences (
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Lecture 03
: Monotone Sequences (
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Lecture 04
: Comparing sequences (
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Lecture 05
: Infinite sums (See this
Numberphile video about series
) (
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)
Lecture 06
: Harmonic series (
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Lecture 07
: Geometric series (
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Lecture 08
: Telescoping series (
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Lecture 09
: The Divergence test (
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Lecture 10
: The ratio test (
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Lecture 11
: Power series (geometric) (
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Lecture 12
: Power Series definition (
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Lecture 13
: New power series from old (
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Lecture 14
: Multiplying power series (
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Lecture 15
: Taylor and Maclaurin series (
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Supplemental Video: Maclaurin and Taylor series (MAT 132 Fall 2011, 11/07/2011) (
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Supplemental Video: The binomial series, etc (MAT 132 Fall 2011, 11/09/2011) (
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Lecture 16
: Shortcuts to compute Taylor series (
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Lecture 17
: Using Taylor series to comute limits (
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Lecture 18
: Binomial series (
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Lecture 19
: Remainder Estimates for Taylor series (
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Lecture 20
: Integrating Taylor Series (
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Lecture 21
: Interval of convergence (
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Lecture 22
: Improper integrals (a quick review) (
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Lecture 23
: The integral test (
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Lecture 24
: p-series and the integral test (
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Lecture 25
: Comparison Test (
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Lecture 26
: The limit comparison test (
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Lecture 27
: Absolute Convergence (
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Lecture 28
: The alternating series test (
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)
Lecture 29
: Introduction to (Ordinary) Differential Equations (
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Lecture 30
: Initial Value Problems (
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Lecture 31
: Slope (direction) fields (
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Lecture 32
: Tutorial about slope-field plotting software (
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Lecture 33
: Euler's Method (
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Lecture 34
: Separation of Variables (
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Lecture 35
: Newton's Law of Cooling (
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Lecture 36
: Models, mostly separable (
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Lecture 37
: Population growth - the Logistic model (
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Lecture 38
: Series solutions to differential equations (
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Lecture 39
: What complex numbers are and why we need them (
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Lecture 40
: The complex exponential and Euler's Formula (
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Lecture 41
: Second order linear equations, part 1 (
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Lecture 42
: Second order linear equations with complex roots (
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)
► MAT 131: Calculus I
About this Course
Lecture 01
: General Information about Functions (
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)
Lecture 02
: Operations on Functions (
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Lecture 03
: Elementary Functions. Part 1 (
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Lecture 04
: Elementary Functions. Part 2 (
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Lecture 05
: Elementary Functions. Part 3 (
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Lecture 06
: Limit and Continuity (
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Lecture 07
: Calculation of Limits (
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)
Lecture 08
: Infinite Limits (
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Lecture 09
: Limits at Infinity (
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)
Lecture 10
: The Derivative. Part 1 (
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Lecture 11
: The Derivative. Part 2 (
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Lecture 12
: Differentiation Rules. Part 1 (
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Lecture 13
: Differentiation Rules. Part 2 (
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Lecture 14
: Derivatives of Trigonometric Functions (
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Lecture 15
: Derivatives of Inverse Functions (
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Lecture 16
: Linearization (
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)
Lecture 17
: Maxima and Minima (
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Lecture 18
: Mean Value Theorem (
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Lecture 19
: First Derivative Test (
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Lecture 20
: The Second Derivative Test (
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Lecture 21
: Implicit Differentiation (
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Lecture 22
: Indeterminate Forms and L’Hôpital’s rule (
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)
Lecture 23
: Related Rates (
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)
Lecture 24
: Optimization Problems (
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)
Lecture 25
: Antiderivative and Indefinite Integral (
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)
Lecture 26
: Elementary Integration (
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)
Lecture 27
: Areas of Plane Figures (
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Lecture 28
: The Definite Integral (
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)
Lecture 29
: Riemann Sums. Part 1 (
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Lecture 30
: Riemann Sums. Part 2 (
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Lecture 31
: The Fundamental Theorem of Calculus (
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Lecture 32
: Applications of The Fundamental Theorem (
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Lecture 33
: Integration by Substitution (
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► MAT 132: Calculus II
About this Course
Episode 01
. Integration techniques: What an integral is (
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)
Episode 02
. Integration techniques: Integration by substitution (
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Episode 03
. Integration techniques: Integration by parts (
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)
Episode 04
. Integration techniques: Integrating rational functions (
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Episode 05
. Integration techniques: Integrating trigonometric functions (
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Episode 06
. Integration techniques: Average value of a function (
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)
Episode 07
. Integration techniques: Improper integrals of type I (
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)
Episode 08
. Integration techniques: Improper integrals of type II (
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)
Episode 09
. Applications of integrals: Area between curves (
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)
Episode 10
. Applications of integrals: Area enclosed by a polar curve (
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)
Episode 11
. Applications of integrals: Area enclosed by parametric curve (
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)
Episode 12
. Applications of integrals: Arc length (
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)
Episode 13
. Applications of integrals: Volume by slicing (
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)
Episode 14
. Applications of integrals: Volume by cylindrical shells (
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)
Episode 15
. Applications of integrals: Mechanical work (
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)
Episode 16
. Applications of integrals: Work to erect The Great Pyramid (
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)
Episode 17
. Differential equations: Separable equations (
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)
Episode 18
. Differential equations: Direction fields and solution curves (
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)
Episode 19
. Differential equations: Orthogonal trajectories (
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)
Episode 20
. Differential equations: Euler's method (
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)
Episode 21
. Differential equations: Mixing problems (
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)
Episode 22
. Differential equations: Newton's law of cooling (
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)
Episode 23
. Differential equations: Exponential growth and decay (
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)
Episode 24
. Differential equations: Logistic model (
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)
Episode 25
. Differential equations: Second order differential equations (
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)
Episode 26
. Sequences and series: Sequences (
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)
Episode 27
. Sequences and series: Model sequences (
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)
Episode 28
. Sequences and series: Limit of a sequence (
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)
Episode 29
. Sequences and series: Series (
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)
Episode 30
. Sequences and series: Divergence test (
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Episode 31
. Sequences and series: Convergence tests (
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)
Episode 32
. Sequences and series: Ratio and root tests (
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)
Episode 33
. Sequences and series: Alternating series test (
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)
Episode 34
. Power series: Power series (
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)
Episode 35
. Power series: Operations on power series (
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)
Episode 36
. Power series: Presentation of functions as power series (
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)
Episode 37
. Power series: Applications of power series (
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,
)
Episode 38
. Power series: Taylor series (
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)
Episode 39
. Power series: Taylor polynomials (
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)
Episode 40
. Power series: Maclaurin series for trigonometric functions (
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,
)
Episode 41
. Power series: Binomial series (
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)
Episode 42
. Power series: Applications of Taylor series (
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,
)