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Calculus I
- 1-1 · Functions
- 1-2 · Inverse Functions
- 1-3 · Trig Functions
- 1-4 · Solving Trig Equations
- 1-5 · Solving Trig Equations with Calculators, Part I
- 1-6 · Solving Trig Equations with Calculators, Part II
- 1-7 · Exponential Functions
- 1-8 · Logarithm Functions
- 1-9 · Exponential and Logarithm Equations
- 1-10 · Common Graphs
- 2-1 · Tangent Lines and Rates of Change
- 2-2 · The Limit
- 2-3 · One–Sided Limits
- 2-4 · Limits Properties
- 2-5 · Computing Limits
- 2-6 · Infinite Limits
- 2-7 · Limits at Infinity, Part I
- 2-8 · Limits At Infinity, Part II
- 2-9 · Continuity
- 2-10 · The Definition of the Limit
- 3-1 · The Definition of the Derivative
- 3-2 · Interpretation of the Derivative
- 3-3 · Differentiation Formulas
- 3-4 · Product and Quotient Rule
- 3-5 · Derivatives of Trig Functions
- 3-6 · Derivatives of Exponential and Logarithm Functions
- 3-7 · Derivatives of Inverse Trig Functions
- 3-8 · Derivatives of Hyperbolic Functions
- 3-9 · Chain Rule
- 3-10 · Implicit Differentiation
- 3-11 · Related Rates
- 3-12 · Higher Order Derivatives
- 3-13 · Logarithmic Differentiation
- 4-1 · Rates of Change
- 4-2 · Critical Points
- 4-3 · Minimum and Maximum Values
- 4-4 · Finding Absolute Extrema
- 4-5 · The Shape of a Graph, Part I
- 4-6 · The Shape of a Graph, Part II
- 4-7 · The Mean Value Theorem
- 4-8 · Optimization
- 4-9 · More Optimization
- 4-10 · L’Hospital’s Rule and Indeterminate Forms
- 4-11 · Linear Approximations
- 4-12 · Differentials
- 4-13 · Newton’s Method
- 4-14 · Business Applications
- 5-1 · Indefinite Integrals
- 5-2 · Computing Indefinite Integrals
- 5-3 · Substitution Rule for Indefinite Integrals
- 5-4 · More Substitution Rule
- 5-5 · Area
- 5-6 · Definition of the Definite Integral
- 5-7 · Computing Definite Integrals
- 5-8 · Substitution Rule for Definite Integrals
- 6-1 · Average Function Value
- 6-2 · Area Between Curves
- 6-3 · Volumes of Solids of Revolution Method of Rings
- 6-4 · Volumes of Solids of Revolution Method of Cylinders
- 6-5 · More Volume Problems
- 6-6 · Work
- 7-1 · Proof of Various Limit Properties
- 7-2 · Proof of Various Derivative Properties
- 7-3 · Proof of Trig Limits
- 7-4 · Proofs of Derivative Applications Facts
- 7-5 · Proof of Various Integral Properties
- 7-6 · Area and Volume Formulas
- 7-7 · Types of Infinity
- 7-8 · Summation Notation
- 7-9 · Constant of Integration
Calculus II
- 1-1 · Integration by Parts
- 1-2 · Integrals Involving Trig Functions
- 1-3 · Trig Substitutions
- 1-4 · Partial Fractions
- 1-5 · Integrals Involving Roots
- 1-6 · Integrals Involving Quadratics
- 1-7 · Integration Strategy
- 1-8 · Improper Integrals
- 1-9 · Comparison Test for Improper Integrals
- 1-10 · Approximating Definite Integrals
- 2-1 · Arc Length
- 2-2 · Surface Area
- 2-3 · Center of Mass
- 2-4 · Hydrostatic Pressure and Force
- 2-5 · Probability
- 3-1 · Parametric Equations and Curves
- 3-2 · Tangents with Parametric Equations
- 3-3 · Area with Parametric Equations
- 3-4 · Arc Length with Parametric Equations
- 3-5 · Surface Area with Parametric Equations
- 3-6 · Polar Coordinates
- 3-7 · Tangents with Polar Coordinates
- 3-8 · Area with Polar Coordinates
- 3-9 · Arc Length with Polar Coordinates
- 3-10 · Surface Area with Polar Coordinates
- 3-11 · Arc Length and Surface Area Revisited
- 4-1 · Sequences
- 4-2 · More on Sequences
- 4-3 · Series - The Basics
- 4-4 · Convergence and Divergence of Series
- 4-5 · Special Series
- 4-6 · Integral Test
- 4-7 · Comparison and Limit Comparison Tests
- 4-8 · Alternating Series Test
- 4-9 · Absolute Convergence and Divergence
- 4-10 · Ratio Test
- 4-11 · Root Test
- 4-12 · Strategy for Series
- 4-13 · Estimating the Value of a Series
- 4-14 · Power Series
- 4-15 · Power Series and Functions
- 4-16 · Taylor Series
- 4-17 · Applications of Series
- 4-18 · Binomial Series
- 5-1 · Vectors - The Basics
- 5-2 · Vector Arithmetic
- 5-3 · Dot Product
- 5-4 · Cross Product
- 6-1 · The 3-D Coordinate System
- 6-2 · Equations of Lines
- 6-3 · Equations of Planes
- 6-4 · Quadric Surfaces
- 6-5 · Functions of Several Variables
- 6-6 · Vector Functions
- 6-7 · Calculus with Vector Functions
- 6-8 · Tangent, Normal and Binormal Vectors
- 6-9 · Arc Length with Vector Functions
- 6-10 · Curvature
- 6-11 · Velocity and Acceleration
- 6-12 · Cylindrical Coordinates
- 6-13 · Spherical Coordinates
Calculus III
- 1-1 · The 3-D Coordinate System
- 1-2 · Equations of Lines
- 1-3 · Equations of Planes
- 1-4 · Quadric Surfaces
- 1-5 · Functions of Several Variables
- 1-6 · Vector Functions
- 1-7 · Calculus with Vector Functions
- 1-8 · Tangent, Normal and Binormal Vectors
- 1-9 · Arc Length with Vector Functions
- 1-10 · Curvature
- 1-11 · Velocity and Acceleration
- 1-12 · Cylindrical Coordinates
- 1-13 · Spherical Coordinates
- 2-1 · Limits
- 2-2 · Partial Derivatives
- 2-3 · Interpretations of Partial Derivatives
- 2-4 · Higher Order Partial Derivatives
- 2-5 · Differentials
- 2-6 · Chain Rule
- 2-7 · Directional Derivatives
- 3-1 · Tangent Planes and Linear Approximations
- 3-2 · Gradient Vector, Tangent Planes and Normal Lines
- 3-3 · Relative Minimums and Maximums
- 3-4 · Absolute Minimums and Maximums
- 3-5 · Lagrange Multipliers
- 4-1 · Double Integrals
- 4-2 · Iterated Integrals
- 4-3 · Double Integrals over General Regions
- 4-4 · Double Integrals in Polar Coordinates
- 4-5 · Triple Integrals
- 4-6 · Triple Integrals in Cylindrical Coordinates
- 4-7 · Triple Integrals in Spherical Coordinates
- 4-8 · Change of Variables
- 4-9 · Surface Area
- 4-10 · Area and Volume Revisited
- 5-1 · Vector Fields
- 5-2 · Line Integrals - Part I
- 5-3 · Line Integrals - Part II
- 5-4 · Line Integrals of Vector Fields
- 5-5 · Fundamental Theorem for Line Integrals
- 5-6 · Conservative Vector Fields
- 5-7 · Green's Theorem
- 6-1 · Curl and Divergence
- 6-2 · Parametric Surfaces
- 6-3 · Surface Integrals
- 6-4 · Surface Integrals of Vector Fields
- 6-5 · Stokes' Theorem
- 6-6 · Divergence Theorem
Differential Equations
- 1-1 · Definitions
- 1-2 · Direction Fields
- 1-3 · Final Thoughts
- 2-1 · Linear Equations
- 2-2 · Separable Equations
- 2-3 · Exact Equations
- 2-4 · Bernoulli Differential Equations
- 2-5 · Substitutions
- 2-6 · Intervals of Validity
- 2-7 · Modeling with First Order DE’s
- 2-8 · Equilibrium Solutions
- 2-9 · Euler’s Method
- 3-1 · Basic Concepts
- 3-2 · Real & Distinct Roots
- 3-3 · Complex Roots
- 3-4 · Repeated Roots
- 3-5 · Reduction of Order
- 3-6 · Fundamental Sets of Solutions
- 3-7 · More on the Wronskian
- 3-8 · Nonhomogeneous Differential Equations
- 3-9 · Undetermined Coefficients
- 3-10 · Variation of Parameters
- 3-11 · Mechanical Vibrations
- 4-1 · The Definition
- 4-2 · Laplace Transforms
- 4-3 · Inverse Laplace Transforms
- 4-4 · Step Functions
- 4-5 · Solving IVP’s with Laplace Transforms
- 4-6 · Nonconstant Coefficient IVP’s
- 4-7 · IVP’s With Step Functions
- 4-8 · Dirac Delta Function
- 4-9 · Convolution Integrals
- 4-10 · Table Of Laplace Transforms
- 5-1 · Review : Systems of Equations
- 5-2 · Review : Matrices & Vectors
- 5-3 · Review : Eigenvalues & Eigenvectors
- 5-4 · Systems of Differential Equations
- 5-5 · Solutions to Systems
- 5-6 · Phase Plane
- 5-7 · Real Eigenvalues
- 5-8 · Complex Eigenvalues
- 5-9 · Repeated Eigenvalues
- 5-10 · Nonhomogeneous Systems
- 5-11 · Laplace Transforms
- 5-12 · Modeling
- 6-1 · Review : Power Series
- 6-2 · Review : Taylor Series
- 6-3 · Series Solutions
- 6-4 · Euler Equations
- 7-1 · Basic Concepts for nth Order Linear Equations
- 7-2 · Linear Homogeneous Differential Equations
- 7-3 · Undetermined Coefficients
- 7-4 · Variation of Parameters
- 7-5 · Laplace Transforms
- 7-6 · Systems of Differential Equations
- 7-7 · Series Solutions
- 8-1 · Boundary Value Problems
- 8-2 · Eigenvalues and Eigenfunctions
- 8-3 · Periodic Functions & Orthogonal Functions
- 8-4 · Fourier Sine Series
- 8-5 · Fourier Cosine Series
- 8-6 · Fourier Series
- 8-7 · Convergence of Fourier Series
- 9-1 · The Heat Equation
- 9-2 · The Wave Equation
- 9-3 · Terminology
- 9-4 · Separation of Variables
- 9-5 · Solving the Heat Equation
- 9-6 · Heat Equation with Non-Zero Temperature Boundaries
- 9-7 · Laplace's Equation
- 9-8 · Vibrating String
- 9-9 · Summary of Separation of Variables