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Calculus Notes
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Contents
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I
Calculus I
1
Intro to Calculus
Intro to Limits
Algebraic Approach to Limits
End Behavior
Continuity
Limits of Trig Functions
2
Derivatives
Intro to Derivatives
Differentiation Techniques
Products and Quotients of Functions
Trig Functions
Chain Rule
Implicit Differentiation
Related Rates
Local Linear Approximation Differential
3
Applications of Derivatives
Applications of Derivatives
Relative Extrema
Absolute Extrema
Applied Max-Min Problems
4
Integrals
Intro to Integrals
Integration by Substitution
Area and Definite Integrals
Fundamental Theorum of Calculus
Definite Integrals with U-Substitution
II
Calculus II
5
Applications of Definite Integrals
Area Between Two Curves
Volumes by Slicing
Arc Length and Surface Area
Work
6
Exponential, Logarithmic and Inverse Trigonometric Functions
Exponential and Logrithmic Functions
Derivatives and Integrals Involving Log Functions
Inverse Functions
L'Hopital's Rule
Inverse Trig Functions
Hyperbolic Trig Functions
7
Principles of Integral Evaluation
Integration by Parts
Integrating Trig Functions
Trig Substitution
Partial Fractions
Improper Integrals
8
Differential Equations
Intro to Differential Equations
III
Calculus III
9
Infinite Series
Sequences
Monotone Sequence
Infinite Series
Convergence Tests
Comparison, Ratio, and Root Tests
Alternating Series; Conditional and Absolute Convergence
Maclaurin and Taylor Polynomials
Maclaurin and Taylor Series; Power Series
Differentiation and Integrating Power Series
10
Parametric and Polar Curves; Conic Sections
Parametric Equations, Tangent Lines, and Arc Length for Parametric Curves
Polar Coordinates
Tangent Lines, Arc Length, and Area for Polar Coordinates
11
Three-Dimentional Space; Vectors
Rectangle Coordinates in 3D Space; Cylindrical Surfaces
Vectors
Dot Products and Projections
Cross Product
Parametric Equations of Lines
Planes in 3-Space
Quadric Surfaces
Cylindrical and Spherical Coordinates
12
Vector-Values Functions
Vector-Valued Functions
Calculus of Vector-Valued Functions
Change of Parameter; Arc Length
Unit Tangent, Unit Normal, and Binomial Vectors
Curvature
IV
Calculus IV (*)
Authored in PreTeXt
Section
10.1
Parametric Equations, Tangent Lines, and Arc Length for Parametric Curves