# Stony Brook MathematicsCourse Videos

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► MAP 102/103: Proficiency Algebra
• Lecture 01: Numbers and Operations  (, , , )
• Lecture 02: Numerical Expressions  (, , , )
• Lecture 03: Variables and Algebraic Expressions  (, , , )
• Lecture 04: Addition and Multiplication  (, , , )
• Lecture 05: Subtraction and Division  (, , , )
• Lecture 06: Distributivity  (, , , )
• Lecture 07: Powers  (, , , )
• Lecture 08: Power Rules  (, , , )
• Lecture 09: Polynomials  (, , , )
• Lecture 10: Operations with Polynomials  (, , , )
• Lecture 11: Rational Expressions  (, , , )
• Lecture 12: Operations with Rational Expressions  (, , , )
• Lecture 13: Composing Algebraic Expressions  (, , , )
• Lecture 14: Equalities, Identities and Equations  (, , , )
• Lecture 15: Linear Equations  (, , , )
• Lecture 16: Applications of Linear Equations  (, , , )
• Lecture 17: Linear Inequalities  (, , , )
• Lecture 18: Absolute Value  (, , , )
• Lecture 19: Lines on a Plane. Part 1  (, )
• Lecture 20: Lines on a Plane. Part 2  (, , , )
• Lecture 21: Linear Systems. Part 1  (, , , )
• Lecture 22: Linear Systems. Part 2  (, , , )
• Lecture 23: Linear Systems. Part 3  (, , , )
• Lecture 24: Radicals  (, , , )
• Lecture 25: Radicals as Powers with Rational Exponents  (, , , )
• Lecture 26: Quadratic Equations  (, , , )
• Lecture 27: Quadratic Formula  (, , , )
• Lecture 28: Factoring Quadratic Polynomials  (, , , )
• Lecture 29: Equations Reducible to Quadratic  (, , , )
• Lecture 30: Parabolas  (, , , )
• Lecture 31: Quadratic Inequalities  (, , , )

► MAT 122: Overview of Calculus
• Lecture 03: Functions and Interval Notation (September 1, 2017)   (, )
• Lecture 04: Linear Functions (September 6, 2017)   (, , )
• Lecture 05: Quadratics and Other Functions (September 8, 2017)   (, )
• Lecture 06: Mathematical Modeling (September 11, 2017)   (, , )
• Lecture 07: Limits (September 13, 2017)   (, )
• Lecture 08: More Limits (September 15, 2017)   (, )
• Lecture 09: Still More Limits and Continuity (September 18, 2017)   (, , )
• Lecture 10: The Definition of the Derivative (September 20, 2017)   (, )
• Lecture 11: More Definition of the Derivative (September 22, 2017)   (, )
• Lecture 12: The Power Rule (September 25, 2017)   (, , )
• Lecture 13: Equation of Tangent Lines (September 25, 2017)   (, )
• Lecture 15: Review of Midterm 1 (October 2, 2017)   (, )
• Lecture 17: Going over the midterm (October 6, 2017)   (, , )
• Lecture 18: The Product and Quotient Rules (October 9, 2017)   (, )
• Lecture 19: The Chain Rule (October 11, 2017)   (, )
• Lecture 20: Tangent Lines, Higher Derivatives, and Concavity (October 13, 2017)   (, , )
• Lecture 21: Maxima and Minima (October 16, 2017)   (, )
• Lecture 22: Curve Sketching (October 18, 2017)   (, , )
• Lecture 23: More Curve Sketching (October 20, 2017)   (, )
• Lecture 24: Curve sketching of difficult functions (October 23, 2017)   (, , )
• Lecture 25: Exponentials and logarithms (October 25, 2017)   (, )
• Lecture 26: Midterm review, part 1 (October 27, 2017)   (, )
• Lecture 27: Midterm review, part 2 (October 30, 2017)   ()
• Lecture 28: going over midterm 2 (November 1, 2017)   (, , )
• Lecture 29: Antiderivatives (November 3, 2017)   (, )
• Lecture 30: More antiderivatives and word problems (November 6, 2017)   (, , )
• Lecture 32: Riemann sums (November 10, 2017)   (, )
• Lecture 33: More Riemann sums (November 10, 2017)   (, , )
• Lecture 34: The Fundamental Theorem of Calculus (November 15, 2017)   (, )
• Lecture 35: Average Value (November 17, 2017)   (, , )
• Lecture 37: Integration (November 27, 2017)   (, )
• Lecture 38: Integration by substitution (November 29, 2017)   (, , )
• Lecture 39: Substitution and Word Problems (December 01, 2017)   (, )
• Lecture 40: Final exam review, part 1 (December 04, 2017)   (, )
• Lecture 41: Final exam review, part 2 (December 06, 2017)   (, )
• Lecture 42: Final exam review, part 3 (December 08, 2017)   (, , )

► MAT 123: Precalculus
• Definition of Sine and Cosine (in Right Triangles)  (, )
• The SOH CAH TOA mnemonic  (, , )
• Lecture 01: Introduction to Trigonometry   (, , )
• Trig values for special angles  (, )
• Lecture 02: Right-triangle Trigometry   (, , )
• The unit circle and trigonometry  (, , , )
• Radian measure  (, , )
• Lecture 03: Radian measure and trig on the unit circle   (, , , )
• Lecture 04: Simple trig identities   (, , )
• Lecture 05: Other trig functions & graphs of sine and cosine   (, , , )
• Graphs of sine and cosine  (, , , )
• Function notation  (, )
• Domain and range  (, )
• Lecture 06: Functions, domain and range   (, , )
• Composition of Functions  (, )
• Lecture 07: Composition of functions   (, , , )
• Lecture 08: Piecewise functions, graph transformations   (, , )
• Inverse Functions  (, )
• Lecture 09: more graph transforms, inverse functions   (, , )
• Lecture 10b: Review for first midterm   (, , )
• Lecture 11: More review   (, , , )
• The Slope of a Line  (, )
• Lecture 12: Lines, circles, and parabolas   (, , , , )
• Rules of Exponents  (, )
• Lecture 13: Exponents, ellipses, polynomial division   (, , )
• Rational functions  (, )
• Lecture 14: Rational functions   (, , , )
• What is a logarithm?  (, )
• Rules for manipulating logarithms  (, )
• Lecture 15: Exponentials and logarithms   (, , )
• Lecture 16: Compound interest, e, and the natural logarithm   (, , , )
• Exponential growth and decay  (, )
• Lecture 17: Exponential growth/decay problems and logs   (, , )
• Lecture 18: Review (logs & exponentials)   (, , )
• Lecture 19: Review for midterm 2   (, , , )
• Lecture 20: Trigonometry review, Law of Sines   (, , )
• Lecture 21: Law of sines, law of cosines, inverse trig functions   (, , , )
• Lecture 22: Inverse trig functions   (, , )
• Lecture 23: Angle sum, double angle, and half-angle formulae   (, , , )
• Lecture 24: More trig&inverse trig; basic graphs   (, , )
• Lecture 25: A garden of graphs   (, , )
• Lecture 26: Graphs and solving equations   (, , , )
• Lecture 27: more equation solving; review   (, , )
• Lecture 28: more review   (, , )
• Final Review:   (, )
• Midterm 1 Review:   (,

► MAT 125: Calculus A
• Lecture 01: Course info and precalculus review. January 28, 2015  (, )
• Introduction to Limits, pre-lecture  (, )
• Definition of the Limit (optional material)  (, )
• Lecture 02: Tangents, velocity, and limits. February 4, 2015  (, )
• Lecture 03: Limits, Limits involving infinity. February 9, 2015  (, )
• Definition of the Derivative, pre-lecture  (, )
• Lecture 04: Limits and Continuity. February 11, 2015  (, , )
• Lecture 05: Definition of the Derivative. February 16, 2015  (, )
• Lecture 06: The function f'(x); what does f' say about f?. February 18, 2015  (, , )
• Midterm I Review Session. February 22, 2015  (, )
• Lecture 07: The power rule & some review. February 23, 2015  (, )
• Lecture 08: Some more review. February 25, 2015  (, , )
• The derivative of exponentials, pre-lecture  (, )
• Lecture 09: The product and quotient rules. March 2, 2015  (, )
• Lecture 10: Derivatives of trigonmetric functions. March 4, 2015  (, , )
• Intuitive explanation of the Chain Rule  (, )
• Lecture 11: The chain rule. March 9, 2015  (, )
• Lecture 12: Implicit differentiation. March 11, 2015  (, )
• Lecture 13: Derivative of logarithmic functions. March 23, 2015  (, )
• Lecture 14: Derivative of inverse trig & logarithmic differentiation. March 25, 2015  (, )
• Midterm II Review Session. March 29, 2015  ()
• Lecture 15: Review for second midterm. March 30, 2015  (, , )
• Lecture 16: Linear approximations and differentials . April 1, 2015  (, )
• Lecture 17: Related rates. April 6, 2015  (, , )
• Lecture 18: More related rates, local maxima/minima . April 8, 2015  (, )
• Lecture 19: Max/min and curve sketching. April 13, 2015  (, , )
• Lecture 20: Derivatives and the shape of curves. April 15, 2015  (, , )
• Lecture 21: Optimization word problems (first 9 minutes of audio missing). April 20, 2015  (, )
• Lecture 22: More optimization, some review. April 22, 2015  (, , )
• Lecture 23: l'Hopital's rule and Newton's method. April 27, 2015  (, , )
• Lecture 24: Antiderivatives. April 29, 2015  (, )
• Lecture 25: some review for final. May 4, 2015  (, )
• Lecture 26: more review. May 6, 2015  (, , )
• Final Review Session . May 11, 2015  (, )

► MAT 126: Calculus B
• Lecture 01: Review of derivatives and basic antiderivatives. January 25, 2016  (, , )
• Lecture 02: Antiderivatives and Riemann Sums. January 27, 2016  (, )
• Lecture 03: Riemann Sums. February 1, 2016  (, , )
• Lecture 04: Definite Integration. February 3, 2016  (, )
• Lecture 05: The Fundamental Theorem of Calculus. February 10, 2016  (, , )
• Lecture 06: The Substitution Rule. February 15, 2016  (, )
• Lecture 07: More Substitution and Midterm 1 Review. February 17, 2016  (, )
• Lecture 08: Midterm 1 Review. February 22, 2016  (, , )
• Lecture 09: Integration by Parts. February 24, 2016  (, , )
• Lecture 10: More Integration by Parts and Trigonometric Integrals. February 29, 2016  (, )
• Lecture 11a: Trig integrals. March 1, 2017  (, )
• Lecture 11b: More trig integrals and trig substitutions. March 6, 2017  (, , )
• Lecture 12: Partial Fraction Decomposition. March 7, 2016  (, )
• Lecture 14: Practicing Integration Techniques. March 21, 2016  (, , )
• Lecture 15: Improper Integrals. March 23, 2016  (, , )
• Lecture 16: Volumes of Revolution - Washers and Discs. March 28, 2016  (, )
• Lecture 17: More Volumes of a Solid of Revolution, and Volumes with known cross-sections. March 30, 2016  (, )
• Lecture 18: More review for Midterm 2 . April 4, 2016  (, )
• Lecture 20: Midterm Exam 2 review. April 11, 2016  (, , )
• Lecture 21: Volume -- Cylindrical Shell Method. April 13, 2016  (, , )
• Lecture 22: Finding Arc Length. April 18, 2016  (, )
• Lecture 23: Average Value of a Function. April 20, 2016  (, , )
• Lecture 24: Applications to Physics and Engineering. April 25, 2016  (, )
• Lecture 25: Finding the hydrostatic force and pressure. April 27, 2016  (, )
• Lecture 26: Review for the Final exam. May 2, 2016  (, )
• Lecture 27: Final Exam Review - Part Two. May 4, 2016  (, , )

► MAT 127: Calculus C
• Lecture 00: Course Introduction - What is MAT127 about?   ()
• Lecture 01: Infinite Sequences   ()
• Lecture 02: Convergence of sequences   ()
• Lecture 03: Monotone Sequences   ()
• Lecture 04: Comparing sequences   ()
• Lecture 05: Infinite sums     (See this Numberphile video about series)  (, )
• Lecture 06: Harmonic series   ()
• Lecture 07: Geometric series   ()
• Lecture 08: Telescoping series   (, )
• Lecture 09: The Divergence test   ()
• Lecture 10: The ratio test   (, )
• Lecture 11: Power series (geometric)   ()
• Lecture 12: Power Series definition   ()
• Lecture 13: New power series from old   ()
• Lecture 14: Multiplying power series   (, )
• Lecture 15: Taylor and Maclaurin series   ()
• Supplemental Video: Maclaurin and Taylor series (MAT 132 Fall 2011, 11/07/2011)   ()
• Supplemental Video: The binomial series, etc (MAT 132 Fall 2011, 11/09/2011)   ()
• Lecture 16: Shortcuts to compute Taylor series   ()
• Lecture 17: Using Taylor series to comute limits   (, )
• Lecture 18: Binomial series   ()
• Lecture 19: Remainder Estimates for Taylor series   (, )
• Lecture 20: Integrating Taylor Series   ()
• Lecture 21: Interval of convergence   ()
• Lecture 22: Improper integrals (a quick review)   ()
• Lecture 23: The integral test   ()
• Lecture 24: p-series and the integral test   ()
• Lecture 25: Comparison Test   (, )
• Lecture 26: The limit comparison test   ()
• Lecture 27: Absolute Convergence   ()
• Lecture 28: The alternating series test   (, )
• Lecture 29: Introduction to (Ordinary) Differential Equations   ()
• Lecture 30: Initial Value Problems   ()
• Lecture 31: Slope (direction) fields   ()
• Lecture 32: Tutorial about slope-field plotting software   ()
• Lecture 33: Euler's Method   (, )
• Lecture 34: Separation of Variables   (, )
• Lecture 35: Newton's Law of Cooling   ()
• Lecture 36: Models, mostly separable   ()
• Lecture 37: Population growth - the Logistic model   (, )
• Lecture 38: Series solutions to differential equations   (, )
• Lecture 39: What complex numbers are and why we need them   ()
• Lecture 40: The complex exponential and Euler's Formula   ()
• Lecture 41: Second order linear equations, part 1   ()
• Lecture 42: Second order linear equations with complex roots   (, )

► MAT 131: Calculus I
• Lecture 01: General Information about Functions  (, )
• Lecture 02: Operations on Functions  (, , )
• Lecture 03: Elementary Functions. Part 1  (, )
• Lecture 04: Elementary Functions. Part 2  (, )
• Lecture 05: Elementary Functions. Part 3  (, , )
• Lecture 06: Limit and Continuity  (, )
• Lecture 07: Calculation of Limits  (, , )
• Lecture 08: Infinite Limits  (, )
• Lecture 09: Limits at Infinity  (, , )
• Lecture 10: The Derivative. Part 1  (, )
• Lecture 11: The Derivative. Part 2  (, , )
• Lecture 12: Differentiation Rules. Part 1  (, )
• Lecture 13: Differentiation Rules. Part 2  (, , )
• Lecture 14: Derivatives of Trigonometric Functions  (, )
• Lecture 15: Derivatives of Inverse Functions  (, , )
• Lecture 16: Linearization  (, )
• Lecture 17: Maxima and Minima  (, )
• Lecture 18: Mean Value Theorem  (, , )
• Lecture 19: First Derivative Test  (, )
• Lecture 20: The Second Derivative Test  (, , )
• Lecture 21: Implicit Differentiation  (, )
• Lecture 22: Indeterminate Forms and L’Hôpital’s rule  (, , )
• Lecture 23: Related Rates  (, , )
• Lecture 24: Optimization Problems  (, , )
• Lecture 25: Antiderivative and Indefinite Integral  (, )
• Lecture 26: Elementary Integration  (, , )
• Lecture 27: Areas of Plane Figures  (, )
• Lecture 28: The Definite Integral  (, , )
• Lecture 29: Riemann Sums. Part 1  (, )
• Lecture 30: Riemann Sums. Part 2  (, , )
• Lecture 31: The Fundamental Theorem of Calculus  (, )
• Lecture 32: Applications of The Fundamental Theorem  (, , )
• Lecture 33: Integration by Substitution  (, , )

► MAT 132: Calculus II
• Episode 01. Integration techniques: What an integral is  (, )
• Episode 02. Integration techniques: Integration by substitution  (, )
• Episode 03. Integration techniques: Integration by parts  (, , )
• Episode 04. Integration techniques: Integrating rational functions  (, )
• Episode 05. Integration techniques: Integrating trigonometric functions  (, )
• Episode 06. Integration techniques: Average value of a function  (, , )
• Episode 07. Integration techniques: Improper integrals of type I  (, )
• Episode 08. Integration techniques: Improper integrals of type II  (, , )
• Episode 09. Applications of integrals: Area between curves  (, )
• Episode 10. Applications of integrals: Area enclosed by a polar curve  (, )
• Episode 11. Applications of integrals: Area enclosed by parametric curve  (, )
• Episode 12. Applications of integrals: Arc length  (, , )
• Episode 13. Applications of integrals: Volume by slicing  (, )
• Episode 14. Applications of integrals: Volume by cylindrical shells  (, , )
• Episode 15. Applications of integrals: Mechanical work  (, )
• Episode 16. Applications of integrals: Work to erect The Great Pyramid  (, , )
• Episode 17. Differential equations: Separable equations  (, )
• Episode 18. Differential equations: Direction fields and solution curves  (, , )
• Episode 19. Differential equations: Orthogonal trajectories  (, )
• Episode 20. Differential equations: Euler's method  (, , )
• Episode 21. Differential equations: Mixing problems  (, )
• Episode 22. Differential equations: Newton's law of cooling  (, )
• Episode 23. Differential equations: Exponential growth and decay  (, )
• Episode 24. Differential equations: Logistic model  (, , )
• Episode 25. Differential equations: Second order differential equations  (, , )
• Episode 26. Sequences and series: Sequences  (, )
• Episode 27. Sequences and series: Model sequences  (, )
• Episode 28. Sequences and series: Limit of a sequence  (, , )
• Episode 29. Sequences and series: Series  (, )
• Episode 30. Sequences and series: Divergence test  (, )
• Episode 31. Sequences and series: Convergence tests  (, , )
• Episode 32. Sequences and series: Ratio and root tests  (, )
• Episode 33. Sequences and series: Alternating series test  (, , )
• Episode 34. Power series: Power series  (, )
• Episode 35. Power series: Operations on power series  (, )
• Episode 36. Power series: Presentation of functions as power series  (, )
• Episode 37. Power series: Applications of power series  (, , )
• Episode 38. Power series: Taylor series  (, )
• Episode 39. Power series: Taylor polynomials  (, )
• Episode 40. Power series: Maclaurin series for trigonometric functions  (, , )
• Episode 41. Power series: Binomial series  (, )
• Episode 42. Power series: Applications of Taylor series  (, , )