I haven't written up notes on all the topics in my calculus courses, and some of these notes are incomplete --- they may contain just a few examples, with little exposition and few proofs. *Be sure to get the PDF files if you want to print them!*

- Notes on first semester calculus - Single-variable calculus: Limits, derivatives, applications of derivatives, basic integration
- Notes on second semester calculus - Single variable calculus: Integration techniques, applications of integration, numerical sequences and series, power series, parametric equations, polar coordinates
- Notes on third semester calculus - [in progress!] Multivariable calculus: Vectors, matrices, determinants, lines and planes, curves and surfaces, derivatives for functions of several variables, maxima and minima, Lagrange multipliers, multiple integrals, volumes and surface area, vector integral calculus

These are notes for 1st semester calculus.

*[09--14--2018]* The notes for Calc 1 have been revised through the section on implicit differentiation.

- Introduction to limits:
informal computations, graphical and numerical evidence.

[PDF file] - The epsilon-delta definition of a limit

[PDF file] - Properties of limits (no proofs)

[PDF file] - Limit theorems - proofs of many of the theorems on limits (
*theory - not required for first-term calculus*)

[PDF file] - Left and right-hand limits; infinite limits

[PDF file] - Continuity; the Intermediate Value Theorem

[PDF file] - Limits at infinity; horizontal and vertical asymptotes

[PDF file] - Derivatives, tangent lines, and rates of change

[PDF file] - Differentiation rules (through the Product Rule and Quotient Rule)

[PDF file] - The Chain Rule

[PDF file] - Trig limits and derivatives

[PDF file] - Inverse
functions and the derivative of an inverse

[PDF file] - Derivatives of log and exponential functions

[PDF file] - Implicit differentiation

[PDF file] - Related rates

[PDF file] - The Mean Value Theorem

[PDF file] - Differentials

[PDF file] - Newton's method

[PDF file] - Absolute maxima and minima

[PDF file] - Increasing and decreasing
functions

[PDF file] - Concavity

[PDF file] - Graphing curves

[PDF file] - Antiderivatives

[PDF file] - Substitution

[PDF file] - Sums and summation notation

[PDF file] - An example involving a
rectangle sum

[PDF file] - Definite integrals

[PDF file] - The Fundamental Theorem
(examples only)

[PDF file] - Area between curves
(see the area notes for 2nd-semester calculus as well)

[PDF file] - Calculus of the natural
logarithm; logarithmic differentiation

[PDF file] - Inverse trig functions

[PDF file]

These are notes for 2nd-semester calculus.

- Integration by parts

[PDF file]

Integration by parts - part 1 [video; 28 min., 32 MB]

Integration by parts - part 2 [video; 19 min., 22 MB] - Integrating trig functions

[PDF file] - Trig substitution

[PDF file] - Partial fractions

[PDF file] - Miscellaneous substitutions
and completing the square

[PDF file] - Review problems on integration
techniques

[PDF file] - L'Hopital's Rule

[PDF file] - Improper integrals

[PDF file] - Finding the area between curves

[PDF file] - Volumes of revolution: circular
slices and washers

[PDF file] - Work

[PDF file] - Sequences

[PDF file] - Infinite series: Geometric
series, convergence, the Zero Limit Test, p-series, and the
Integral Test

[PDF file] - Direct comparsion and limit
comparison

[PDF file] - The Ratio Test and the
Root Test

[PDF file] - Alternating series

[PDF file] - Absolute convergence and
conditional convergence

[PDF file] - Convergence of infinite (numerical) series review

[PDF file]

Convergence of infinite (numerical) series review - part 1 [video: 28 MB, 24 min]

Convergence of infinite (numerical) series review - part 2 [video: 30 MB, 25 min] - Intervals
of convergence of power series

[PDF file] - Taylor series

[PDF file] - The Remainder Term for
Taylor series

[PDF file] - Power series review

[PDF file]

Power series review - part 1 [video: 29 MB, 25 min]

Power series review - part 2 [video: 30 MB, 25 min] - Parametric equations

[PDF file] - Polar coordinates

[PDF file] - Arc length in polar coordinates

[PDF file]

These are notes for 3rd-semester calculus. They were written during Spring, 2018.

- Points in 2 and 3-dimensional Euclidean space

[PDF file] - Vectors

[PDF file] - Dot products

[PDF file] - Matrices

[PDF file] - Determinants

[PDF file] - Cross products

[PDF file] - Lines and planes

[PDF file] - Distance problems involving lines and planes

[PDF file] - Surfaces

[PDF file] - Parametric surfaces

[PDF file] - Vector functions

[PDF file] - Parametric curves

[PDF file] - Velocity and acceleration

[PDF file] - Arc length

[PDF file] - Unit tangent, unit normal, binormal; curvature; osculating circle

[PDF file] - Functions of several variables

[PDF file] - Limits and continuity

[PDF file] - Partial derivatives

[PDF file] - Tangent planes and normal lines

[PDF file] - Derivatives of functions of several variables

[PDF file] - The Chain Rule for functions of several variables

[PDF file] - Taylor series for functions of several variables (brief description - no proofs)

[PDF file] - Directional derivatives and gradients

[PDF file] - Maxima and minima for functions of two variables

[PDF file] - Lagrange multipliers

[PDF file] - Double integrals

[PDF file] - Volumes by double integrals

[PDF file] - Double integrals in polar

[PDF file] - Interchanging the order of integration

[PDF file] - Surface area

[PDF file] - Triple integrals

[PDF file] - Change of variables in multiple integrals

[PDF file] - Cylindrical coordinates

[PDF file]< - Spherical coordinates

[PDF file] - Center of mass

[PDF file] - Gradient, divergence, curl

[PDF file] - Path integrals

[PDF file] - Conservative fields and path independence

[PDF file] - Green's theorem

[PDF file] - Scalar and vector surface integrals; flux

[PDF file] - The Divergence Theorem

[PDF file] - Stokes' Theorem

[PDF file]

Copyright 2018 by Bruce Ikenaga