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Step By Step Calculus - Table of Contents

Offering: Step By Step Calculus

Titles: Step By Step Calculus, Single Variable Calculus Practice Galore, Calculus: Audible Lecture Series, eWorkbook

By Dr. Michael Kouritzin , Dr. Jack Macki , Dr. Shubhashis Ghosh , Dr. Jia Liu , Dr. Lee Keener

  • 1. Introduction
    • 1.0 - Preface
    • 1.1 - Introduction
  • 2. Algebra of Numbers and Sets
    • 2.0 - History and Applications
    • 2.1 - Number System
    • 2.2 - Number Operations
    • 2.3 - Sets of Numbers
    • 2.4 - Set Operations
    • 2.5 - Bounds and Cardinality of Sets
    • 2.6 - The Rectangular Coordinate System
    • 2.7 - Polynomial Functions and Algebra
    • 2.8 - Rational Functions
    • 2.9 - Tricks for Dividing
  • 3. Conic Sections
    • 3.1 - General Conics
    • 3.2 - Parabola
    • 3.3 - Ellipse
    • 3.4 - Hyperbola
  • 4. The Concept of Function
    • 4.0 - History and Applications
    • 4.1 - Function Definition
    • 4.2 - Lines
    • 4.3 - Absolute Value and Piecewise-defined Functions
    • 4.4 - Equalities and Inequalities
    • 4.5 - Composite Functions
    • 4.6 - Symmetry and Transformations of Functions
    • 4.7 - Inverse Functions
    • 4.8 - Inverse of Monotonic Functions
  • 5. Trigonometric Functions
    • 5.1 - Angles and The Unit Circle
    • 5.2 - Sine and Cosine Functions
    • 5.3 - Other Trigonometric Functions
    • 5.4 - Addition and Subtraction Formulae
    • 5.5 - Double and Half Angle Formulae
    • 5.6 - Trigonometry In Equations
  • 6. Applications of Trigonometry and Algebra
    • 6.1 - Right Triangle Trigonometry
    • 6.2 - General Triangles
    • 6.3 - Sketching Trigonometric Functions
    • 6.4 - Inverse Trigonometric Functions
    • 6.5 - Inverse Trigonometric Identities and Applications
  • 7. Exponential Functions, Hyperbolic Functions and Their Inverses
    • 7.1 - Exponential Functions
    • 7.2 - Hyperbolic Functions
    • 7.3 - Logarithmic and Inverse Hyperbolic Functions
  • 8. Introduction to Discrete Mathematics
    • 8.1 - Summation and Product
    • 8.2 - Sequences and Series
    • 8.3 - Induction and Summation Formulae
    • 8.4 - Equally Likely Conditional Probability
    • 8.5 - Permutations and Combinations
    • 8.6 - Multinomial and Hypergeometric Distributions
  • 9. Limits and Continuity
    • 9.0 - History and Applications
    • 9.1 - Squeeze and Monotone Theorems
    • 9.2 - Definition of Limits and Asymptotes
    • 9.3 - Limit Laws
    • 9.4 - Continuous Functions and the Intermediate Value Theorem
    • 9.5 - Limits of Indeterminate Forms
  • 10. Differentiation
    • 10.0 - History and Applications
    • 10.1 - Definition of Derivative
    • 10.2 - Rules for Derivatives
    • 10.3 - Derivatives of Exponential and Logarithmic Functions
    • 10.4 - Derivatives for Hyperbolic and Inverse Functions
    • 10.5 - Derivatives for Trigonometric and Inverse Functions
    • 10.6 - Mean Value Theorem
    • 10.7 - Higher Order Derivatives
    • 10.8 - Implicit Differentiation
  • 11. Partial Differentiation and Applications
    • 11.1 - Two Variable Functions and Implicitly Defined Curves
    • 11.2 - Definition of Partial Derivative
    • 11.3 - Partial Derivative Rules
    • 11.4 - Higher Order Partial Derivatives
    • 11.5 - Implicit Differentiation using Partial Derivative Technique
    • 11.6 - Related Rates
  • 12. Parametric Curves
    • 12.1 - Definition of Integral
    • 12.1 - Introduction to Parametric Curves
    • 12.2 - Continuity
    • 12.3 - Differentiation and Cauchy Mean Value Theorem
  • 13. Analyzing Functions and Curves
    • 13.0 - History and Applications
    • 13.1 - Linear Approximation and Newton's Method
    • 13.2 - Tangent Lines for Curves
    • 13.3 - L'Hospital's Rule
    • 13.4 - Slant Asymptotes
    • 13.5 - Critical Points, Concavity and Extrema
    • 13.6 - Optimization Problems
    • 13.7 - Graph Sketching for Functions
  • 14. Polar Curves
    • 14.0 - History and Applications
    • 14.1 - Polar Co-ordinates and Polar Curves
    • 14.2 - Sketching Polar Curves
    • 14.3 - Conic Sections in Polar Co-ordinates
  • 15. Indefinite Integrals
    • 15.1 - Indefinite Integrals
    • 15.2 - Change of Variables
    • 15.3 - Integration by Parts
    • 15.4 - Integration for Trigonometric Functions
    • 15.5 - Trigonometric versus Polynomial Substitutions
    • 15.6 - Use of Integral Forms
    • 15.7 - Integration by Partial Fractions
  • 16. Differential Equations
    • 16.0 - History and Applications
    • 16.1 - Exponential Growth/Decay
    • 16.2 - Separable Differential Equations
    • 16.3 - Linear Differential Equations
    • 16.4 - Direction Fields, Euler's Method
    • 16.5 - Predator-Prey Systems
  • 17. Series and Applications to Differentiation and Limits
    • 17.0 - History and Applications
    • 17.1 - Infinite Series as a Sequence
    • 17.2 - Integral and Comparison Tests
    • 17.3 - Ratio and Root Tests
    • 17.4 - Alternating Series, Absolute and Conditional Convergence
    • 17.5 - Power Series
    • 17.6 - Taylor Series
    • 17.7 - Taylor Polynomials
    • 17.8 - Root Finding Algorithms
  • 18. Definite Integrals
    • 18.0 - History and Applications
    • 18.1 - Riemann Sums and Definition of Definite Integral
    • 18.2 - Fundamental Theorem of Calculus
    • 18.3 - Arc Length
    • 18.4 - Curvature
    • 18.5 - Work and Fluid Pressure
  • 19. Extended Use of Definite Integrals
    • 19.1 - Area within Closed Curves
    • 19.2 - Areas of Surfaces of Revolution
    • 19.3 - Improper Integrals
    • 19.4 - Probability
    • 19.5 - Numeric Integration
    • 19.6 - Error Bounds in Numeric Integration
  • 20. Volumes
    • 20.1 - Higher Dimensional Cartesian Co-ordinates
    • 20.2 - Volumes by Rotating
    • 20.3 - Mass and Center of Mass
    • 20.4 - Volumes by Slicing
    • 20.5 - Indicator Functions
    • 20.6 - Volumes by Iterated Integration
  • 21. Curves in Space
    • 21.0 - History and Applications
    • 21.1 - Space Vector Algebra
    • 21.2 - Equations of Lines
    • 21.3 - Vector Functions and Space Curves
    • 21.4 - Derivatives and Integrals of Vector Functions
    • 21.5 - Tangents and Normals for Vector Functions
    • 21.6 - Arc Length and Curvature for Vector Functions
    • 21.7 - Torsion of Vector Functions
  • 22. Surfaces in Space
    • 22.1 - Equations of Planes
    • 22.2 - Multivariable Functions, Cylinders and Surfaces
    • 22.3 - Limits of Multi-variables Functions
    • 22.4 - Gradients and Directional Derivatives
    • 22.5 - Tangent Planes and Linear Approximations
    • 22.6 - Maxima and Minima
    • 22.7 - Constrained Optimization and Lagrange Multipliers
  • 23. Higher Dimensional Integration
    • 23.1 - Orientation, Representation and Boundary Curves
    • 23.2 - Double and Iterated Integrals
    • 23.3 - Cylindrical and Spherical Co-ordinates
    • 23.4 - Volumes by Cylindrical Co-ordinates
    • 23.5 - Applications of Double Integrals
    • 23.6 - Triple Integrals
    • 23.7 - Triple Integrals in Cylindrical and Spherical Coordinates
    • 23.8 - Change of Variables in Multiple Integrals
    • 23.9 - Line Integrals
    • 23.10 - Surface Integrals
  • 24. Vector Calculus
    • 24.1 - Vector Fields and Operator
    • 24.2 - The Fundamental Theorem for Line Integrals
    • 24.3 - Green's Theorem
    • 24.4 - Stokes' Theorem
    • 24.5 - The Divergence Theorem