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 [revisions in progress - Fall, 2018]
- Notes on second semester calculus - Single variable calculus: Integration techniques, applications of integration, numerical sequences and series, power series, parametric equations, polar coordinates [old - revisions planned for Spring, 2018]
- Notes on third semester calculus - 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 [written Spring, 2018]

These are notes for 1st semester calculus.

*[12--07--2018]* The notes for Calc 1 have all been revised.

- 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 and the Second Derivative Test

[PDF file] - Graphing curves

[PDF file] - Max-min word problems

[PDF file] - Antiderivatives

[PDF file] - Substitution

[PDF file] - Sums and summation notation

[PDF file] - Rectangle sums

[PDF file] - Definite integrals

[PDF file] - The Fundamental Theorem of Calculus

[PDF file] - The Fundamental Theorem of Calculus - an empirical demonstration using
*Mathematica*

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

[PDF file] - L'Hopital's Rule

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

[PDF file] - Separation of variables (brief introduction)

[PDF file] - Exponential growth and Newton's law of cooling

[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] - 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