### General Calculus and Linear Algebra

© Teresa Hartman

##### Chapter 0 - Review of College Algebra

0.1 Factoring

Common Factor / Factor by Grouping / Trinomial / Difference of Squares / Calculus Examples / Factoring Completely

0.2 Solving Equations

Linear / Factoring Method / Square Root Method

0.3 Solving More Equations

Quadratic Formula / Rational Equations

0.4 Graphing Linear and Quadratic Functions

Linear: Slope / All Equation Forms / Graphing Lines / Writing Equations of Lines

Quadratic: Vertex / X and Y-intercepts / Graphing Parabolas

0.5 Graphing Polynomials

End Behavior / y-intercept / Zeros / Graphing Calculator

0.6 Graphing Rational Equations

y-intercept / x-intercepts / Vertical Asymptote / End Behavior / Graphing Calculator

0.7 Misc

Rationalizing / Piecewise Functions / Domain

##### Chapter 1 - Limits

1.1 Finite Limits

Easy Limits / Form of Constant Divided by 0 / Form of Zero divided by Zero

1.2 Infinite Limits

Visuals of Graphs / Polynomial End Behavior / Face Case with Rational Functions / Calculus Methods

##### Chapter 2 - Differentiation: Basic Concepts

2.1 Applications of the Derivative

2.2 Techniques of Differentiation

##### Chapter 3 - Derivative Applications

3.1 Increasing, Decreasing, and Relative Extrema

3.2 Concavity and Inflection Points

3.3 Second Derivative Test and Sketching Graphs

3.4 Drawing Graphs of all functions

##### Chapter 4- Exponential and Logarithmic Functions

4.1 Exponential Functions; Compound Interest

Review of Exponential Properties / Solving Basic Exponential Equations / Graphing Exponential Functions / Compound Interest / Continuous Interest/ Future and Present Value / Effective Nominal Interest

4.2 Logarithmic Functions and Equations

Rewriting as an Exponent / Properties of Logarithms / Graphing Logarithmic Functions / Solving Equations Containing Exponents and Logarithms

4.3 Differentiation of Exponent and Logarithmic Functions

Derivatives of all Exponential and Logarithmic Functions and their Applications

##### Chapter 5- Linear Algebra

5.1 Substitution and Elimination Method

Graphing Method / Substitution Method / Elimination Method / Parallel and Same Lines / Three-Dimensions / Checking with Graphing Calculator

5.5 Determinants and Cramer's Rules