PSK Lesson Notes

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Elementary Algebra

Introduction to Algebra

Linear Equations and Inequalities

Functions and Graphs I

3.1 Introduction to Graphing
3.2 Solving Equations Graphically
3.3 Functions I - Introduction
3.4 Functions II - Domain, Range, & Operations

Lines and thier Graphs

4.1 Intercept Points
4.2 Slopes
4.3 Equations of Lines I - Slope-Intercept Formula
4.4 Equations of Lines II - Point-Slope Formula
4.5 Graphing Linear Inequalities

Linear Systems

Exponents & Polynomials

Intermediate Algebra

Factoring

Rational Expressions

Rational Equations and Applications

Radical Expressions

10.1 Roots & Radical Functions
10.2 Fractional Exponents
10.3 Operations I - Simplify & Multiply
10.4 Operations II - Add & Subtract
10.5 Operations III - Divide & Rationalize
10.6 Operations IV - Distribute, Foil, & Factor
10.7 Complex Numbers

Nonlinear Equations and Applications

11.1 Radical Equations
11.2 Quadratic Equations I - Root Method
11.3 Quadratic Equations II - Complete the Square
11.4 Quadratic Equations III - Quadratic Formula
11.5 Applications - Geometry & Pythagorean Theorem

Functions and Graphs II

12.1 Parabolas I - Algebraic Approach
12.2 Parabolas II - Graphical Approach
12.3 Functions III - Composite & Inverse

Exponential and Logarithmic Functions

13.1 Exponential Functions & Graphs
13.2 Logarithmic Functions & Graphs
13.3 Properties of Logarithms
13.4 Exponential & Logarithmic Equations
13.5 Applications - Exponentials & Logarithms

Precalculus I / College Algebra

Equations and Inequalitites

Functions and Graphs

Polynomial and Rational Functions

3.1 Quadratic Functions
3.2 Polynomial Functions I - Introduction, Zeros
3.3 Polynomial Functions II - Division, Remainder Thm, Factor Thm
3.4 Polynomial Functions III - Complex Zeros, Fundamental Thm of Algebra, Descartes Rule
3.5 Rational Functions & Graphs
3.6 Partial Fractions

Exponential and Logarithmic Functions

Systems and Matrices

Geometry Basics

6.1 Distance and Midpoint Formulae
6.2 Circles

Conic Sections

Sequences and Series

Precalculus II / Trigonometry

The Six Trigonometric Functions

Right Triangle Trigonometry

Circular Functions

Graphs of Trigonometric Functions

4.1 Basic Graphs
4.2 Amplitude & Period
4.3 Vertical Translations & Phase Shift
4.4 General Equation & Graph to Equation
4.5 Combination Graphs
4.6 Harmonic Motion
4.7 Inverse Trigonometric Functions

Trigonometric Identities

5.1 Proving Trig Identities
5.2 Sum/Difference Identities
5.3 Double-Angle Identities
5.4 Half-Angle Identities
5.5 IDs Involving Inverse Trig Functions

Trigonometric Equations

6.1 Solving Trig Equations
6.2 Equations Involving Identities
6.3 Equations with Multiple Angles
6.4 Equations Involving Inverse Trig Fns

Oblique Triangles and the Laws

Vectors

Complex, Parametric, and Polar Forms

9.1 Trigonometric Form of Complex Numbers
9.2 Products and Quotients in Trig Form
9.3 Powers and Roots in Trig Form
9.4 Parametric Equations and Graphs
9.5 Polar Equations and Graphs

Calculus I

Limits and Continuity

1.0 Introduction to Calculus
1.1 Limits Graphically
1.2 Limits Numerically
1.3 Limits Algebraically
1.4 Delta-Epsilon Proofs
1.5 Properties of Limits
1.6 One-Sided Limits
1.7 Infinite Limits & Vertical Asymptotes
1.8 Limits at Infinity & Horizontal Asymptotes
1.9 Limits Electronically
1.10 Continuity

Derivatives

2.1 Definitions of Derivative
2.2 Rates of Change
2.3 Differentiability
2.4 Derivatives of Basic Functions
2.5 Higher Order Derivatives
2.6 Motion and the Derivative
2.7 Product and Quotient Rules
2.8 Derivatives of Trigonometric Functions
2.9 Chain Rule
2.10 Implicit Differentiation
2.11 Derivatives of Exponential and Logarithmic Functions
2.12 Logarithmic Differentiation
2.13 Derivatives of Inverse Functions
2.14 Derivatives of Inverse Trigonometric Functions
2.15 Electronic Differentiation & Formula Sheets
2.16 Related Rate Applications
2.17 Linear Approx & Differentials
2.18 Newton's Method

Analysis of Curves

3.1 Extreme Values & CPs
3.2 Mean Value Theorem for Derivatives
3.3 First Derivative Test & Increasing/Decreasing Functions
3.4 Second Derivative Test, IPs, & Concavity
3.5 Curve Sketching
3.6 Electronically Analyzing Curves
3.7 Fun with Reform Calculus
3.8 Optimization Applications

Antiderivatives

4.1 Antidifferentiaton
4.2 Summation Notation
4.3 Area Under a Curve
4.4 Riemann Sum Definition of Definite Integral
4.5 Properties of Sums and Definite Integrals
4.6 Definite Integrals Geometrically
4.7 Fundamental Theorems of Calculus

Calculus II

Transcendental Functions

Integration

Geometry

Physics

Integration Techniques

Calculus of Infinity

Parametric, Polar, and Conic Curves

Calculus III

Sequences and Infinite Series

12.0 Intro to Seqs and Series
12.1 Sequences
12.2 Infinite Series
12.3 Special Series
12.4 Divergence Test
12.5 Integral and p-Seies Tests
12.6 Ratio and Root Tests
12.7 Comparison Tests
12.8 Alternating Series
12.9 Absolute and Conditional Convergence
12.10 General Strategy

Power Series

13.1 Taylor Polynomials and Approximations
13.2 Representing Functions as Power Series
13.3 Taylor, Maclaurin, and Binomial Series
13.4 Calculus of Power Series

Vectors and Geometry of Space

14.1 Vectors in 2D
14.2 Rectangular Coordinates and Vectors in 3D
14.3 Dot Product
14.4 Cross Product
14.5 Lines and Curves
14.6 Planes
14.7 Quadric Surfaces

Vector-Valued Functions

15.1 Intro to VV Functions
15.2 Calculus of VV Functions
15.3 Velocity and Acceleration
15.4 Arc Length
15.5 Curvature
15.6 Normal and Binormal Vectors
15.7 Cylindrical and Spherical Coordinates

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