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MATH 144:
Calculus for the Physical Sciences I
Vincent Bouchard
Contents
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Contents
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Front Matter
Preface
1
Review
Algebra
Functions
Analytic geometry
Trigonometry
2
A preview of calculus
A preview of differential and integral calculus from kinematics
Tangent lines and derivatives
3
Limits
An informal definition of limits
The formal definition of limits
Infinite limits and vertical asymptotes
How to evaluate limits
Continuity
Limits at infinity and horizontal asymptotes
4
Differentiation
The derivative of a function
Differentiability
Differentiation rules
Derivatives of trigonometric functions
Chain rule
Implict differentiation
Inverse functions
Exponentials and logarithms
Inverse trigonometric functions
5
Integration
Antiderivatives and indefinite integrals
Area, displacement and Riemann sums
Definite integrals
The Fundamental Theorem of Calculus
Substitution
Areas between curves
6
Functions and curves
The Intermediate Value Theorem
The Mean Value Theorem
Maxima and minima
Curve sketching
7
Applications of differentiation
Related rates
Optimization
Linear approximation
Taylor polynomials
Newton's method
Authored in PreTeXt
Chapter
3
Limits
3.1
An informal definition of limits
3.2
The formal definition of limits
3.3
Infinite limits and vertical asymptotes
3.4
How to evaluate limits
3.5
Continuity
3.6
Limits at infinity and horizontal asymptotes