Skip to main content
\(\DeclareMathOperator{\Tr}{Tr} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)
MATH 144:
Calculus for the Physical Sciences I
Vincent Bouchard
Contents
Prev
Up
Next
Contents
Prev
Up
Next
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
MATH 144:
Calculus for the Physical Sciences I
Vincent Bouchard
University of Alberta
November 9, 2020
These are notes for MATH 144 offered at the University of Alberta.
Preface