### 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