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Calculus Notes
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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
Chapter
2
Derivatives
2.1
Intro to Derivatives
2.2
Differentiation Techniques
2.3
Products and Quotients of Functions
2.4
Trig Functions
2.5
Chain Rule
2.6
Implicit Differentiation
2.7
Related Rates
2.8
Local Linear Approximation Differential