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  • Chapter 1 - Rates of Change and the Derivative
    • Preface
    • 1 - Average Rates of Change
    • 2 - Prelude to Instantaneous Rates of Change
    • 3 - Limits and Continuity
    • 4 - Instantaneous Rates of Change: The Derivative
    • 5 - Extrema and the Mean Value Theorem
    • 6 - Higher-Order Derivatives
  • Chapter 2 - Basic Rules for Calculating Derivatives
    • 1 - The Power Rule for Integer Powers
    • 2 - The Product and Quotient Rules
    • 3 - The Chain Rule
    • 4 - The Exponential Function
    • 5 - The Natural Logarithm
    • 6 - General Exponential and Logarithmic Functions
    • 7 - Trigonometric Functions: Sine and Cosine
    • 8 - The Other Trigonometric Functions
    • 9 - Inverse Trig Functions
    • 10 - Implicitly Defined Functions
  • Chapter 3 - Applications of Differentiation
    • 1 - Related Rates
    • 2 - Graphing
    • 3 - Optimization
    • 4 - Linear Approximation, Differentials, and Newton’s Method
    • 5 - Indeterminate Forms and L´Hôpital’s Rule
  • Chapter 4 - Introduction to Differential Equations
    • 1 - What is a Differential Equation?
    • 2 - Anti-Derivatives
    • 3 - Separable Differential Equations
    • 4 - Applications of Differential Equations
    • 5 - Approximating Solutions of y'=m(x,y)
    • Appendix
    • Video Lectures - Chapter 1 - Anti-differentiation: the Indefinite Integral
      • 1 - Basic Anti-Differentiation
      • 2 - Special Trig. Integral and Trig. Substitutions
      • 3 - Integration by Partial Fractions
      • 4 - Integration using Hyperbolic Sine and Cosine
    • Chapter 2 - Continuous sums: the Definite Integral
      • 1 - Sums and Differences
      • 2 (a) - Prelude to the Definite Integral
      • 2 (b) - Prelude to the Definite Integral (cont.)
      • 3 (a) - The Definite Integral
      • 3 (b) - The Definite Integral
      • 4 - The Fundamental Theorem of Calculus
      • 5 - Improper Integrals
      • 6 - Numerical Techniques for Approximating Integrals
    • Chapter 3 - Applications of Integration
      • 1 - Distance Traveled in a Straight Line
      • 2 - Area in the Plane
      • 3 - Distance Traveled in Space and Arc Length
      • 4 - Area Swept Out and Polar Coordinates
      • 5 - Volume
      • 6 - Surface Area
      • 7 - Mass and Density
      • 8 - Centers of Mass and Moments
      • 9 - Work and Energy
      • 10 - Hydrostatic Pressure
    • Chapter 4 - Understanding Functions via Polynomials and Power Series
      • 1 - Approximating Polynomials
      • 2 - Approximating Functions with Polynomials
      • 3 - Error in Approximation by Polynomials
      • 4 - Functions as Power Series
    • Chapter 5 - Theorems on Sequences and Series
      • 1 - Theorems on Sequences
      • 2 - Theorems on Series (part 1 - Basic Properties)
      • 3 - Theorems on Series (part 2 - Non-negative Series)
      • 4 - Theorems on Series (part 3 - Series with positive and Negative Terms)
      • Appendix A - An introduction to vectors and motion.
    • Chapter 2 - (a) Basics, (b) More Depth, (c) + Linear Algebra.
      • 1 (a) - Partial Derivatives
      • 1 (b) - Partial Derivatives
      • 2 (a) - The Total Derivative
      • 3 (a) - Linear Approximation & the Tangent Plane
      • 3 (b) - Linear Approximation & the Tangent Planes & the Differential
      • 4 (a) - Differentiation Rules
      • 5 (a) - The Directional Derivative
      • 6 (a) - Level Sets & Gradient Values
      • 7 (a) - Change of Coordinates
      • 8 (a) - Parameterizing Surfaces
      • 9 (a) - Local Extrema
      • 10 (a) - Optimization
      • 11 (a) - Lagrange Multipliers
      • 12 (a) - Implicit Differentiation
      • 13 (a) - Multivariable Taylor Polynomials and Series
    • Chapter 3
      • 1 - Partial Anti-Derivatives & Iterated Integrals
      • 2 - Integration in R²
      • 3 - Integration with Polar Coordinates
      • 4 - Integration in R³
      • 5 - Volume
      • 6 - Integration with Cylindrical and Spherical Coordinates
      • 7 - Average Value
      • 8 - Mass & Density
      • 9 - Centers of Mass
      • 10 - Moments of Inertia
      • 11 - Surfaces & Area
    • Chapter 4
      • 1 - Vector Fields
      • 1 - Line Integrals
    • Chapter 1 - Rates of Change and the Derivative
      • 1 - Average Rates of Change
      • 2 - Prelude to Instantaneous Rates of Change
      • 3 - Limits and Continuity
      • 4 - Instantaneous Rates of Change: The Derivative
      • 5 - Extrema and the Mean Value Theorem
      • 6 - Higher-Order Derivatives
    • Chapter 2 - Basic Rules for Calculating Derivatives
      • 1 - The Power Rule for Integer Powers
      • 2 - The Product and Quotient Rules
      • 3 - The Chain Rule
      • 4 - The Exponential Function
      • 5 - The Natural Logarithm
      • 6 - General Exponential and Logarithmic Functions
      • 7 - Trigonometric Functions: Sine and Cosine
      • 8 - The Other Trigonometric Functions
      • 9 - Inverse Trig Functions
      • 10 - Implicitly Defined Functions
    • Chapter 3 - Applications of Differentiation
      • 1 - Related Rates
      • 2 - Graphing
      • 3 - Optimization
      • 4 - Linear Approximation, Differentials, and Newton’s Method
      • 5 - Indeterminate Forms and L´Hôpital’s Rule
    • Chapter 4 - Introduction to Differential Equations
      • 1 - Anti-derivatives and Basic Differential Equations
      • 2 - Applications of Differential Equations
      • 3 - Separable Differential Equations
      • 4 - More Applications of Differential Equations
      • 5 - Approximating Solutions of y'=m(x,y)
    • Chapter 5 - Continuous sums: the Definite Integral
      • 1 - Sums and Differences
      • 2 (a) - Prelude to the Definite Integral
      • 2 (b) - Prelude to the Definite Integral (cont.)
      • 3 (a) - The Definite Integral
      • 3 (b) - The Definite Integral
      • 4 - The Fundamental Theorem of Calculus
      • 5 - Improper Integrals
      • 6 - Numerical Techniques for Approximating Integrals
    • Chapter 6 - Applications of Integration
      • 1 - Distance Traveled in a Straight Line
      • 2 - Area in the Plane
      • 3 - Distance Traveled in Space and Arc Length
      • 4 - Area Swept Out and Polar Coordinates
      • 5 - Volume
      • 6 - Surface Area
      • 7 - Mass and Density
    • Chapter 7 - Understanding Functions via Polynomials and Power Series
      • 1 - Approximating Polynomials
      • 2 - Approximating Functions with Polynomials
      • 3 - Error in Approximation by Polynomials
      • 4 - Functions as Power Series
      • 5 - Power Series as Functions I
      • 6 - Power Series as Functions II
    • Chapter 8 - Theorems on Sequences and Series
      • 1 - Theorems on Sequences
      • 2 - Theorems on Series (part 1 - Basic Properties)
      • 3 - Theorems on Series (part 2 - Non-negative Series)
      • 4 - Theorems on Series (part 3 - Series with positive and Negative Terms)
      • A 1 - Parameterized Curves
  • Aaron Silberstein - Plane Curve Singularities and the Absolute Galois Group of Q
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    • Alina Marian - On the tautological cohomology of the moduli space of curves
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    • Jose Seade - Milnor fibrations for real singularities
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    • Maria Angelica Cueto - Implicitization of surfaces via geometric tropicalization
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    • Thomas Eliot - undergraduate talk
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    • Ryan Reich - On Beilinson's “How to glue perverse sheaves”
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    • Alexandru Suciu - Dwyer-Fried Invariants
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    • Pavel Etingof - D-modules on Poisson varieties and Poisson traces
      • Play video
    • Thomas Koberda - Residual properties of 3-manifold groups
      • Play video
    • Alvise Trevisan - Real quasi-toric manifolds and their homology
      • Play video
    • Steven Kleiman - Equisingularity of germs of isolated singularities
      • Play video
    • Valerio Toledano Laredo - Stability conditions and Stokes Factors
      • Play video
    • Andrei Zelevinsky - Cluster Algebras via Quivers with Potentials
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    • Eriko Hironaka - Lehmer's Problem and Dilatations of Mapping Classes
      • Play video
    • David B. Massey - From the Milnor Number to the Characteristic Cycle of the Vanishing Cycles
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    • Marc Levine - The Motivic Fundamental Group
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    • Paolo Aluffi - Chern Classes of Blow-ups
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    • Lê Dũng Tráng - Equisingularity Problems (click on title for further details)
      • Play video

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