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Kansas State Polytechnic

Kansas State Polytechnic
2310 Centennial Road
Salina, KS 67401-8196

Operator: 785-826-2672
Admissions: 785-826-2640
polytechnic@k-state.edu

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

1.3 One-sided Limits

1.4 Continuous Functions

1.5 The Derivative 


Chapter 2 - Differentiation: Basic Concepts

2.1 Applications of the Derivative

2.2 Techniques of Differentiation

2.3 Product Rule

2.4 Quotient Rule

2.5 Higher-Order Derivatives

2.6 Chain Rule


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

5.2 Matrix Method

5.3 Matrix Algebra

5.4 Inverse of a Matrix

5.5 Determinants and Cramer's Rules