cohtran_appliedmath

College Algebra

 




LECTURE 

1.1            FUNCTIONS , GRAPHS  
Topics : 
- Graphs , tables and equations that represent functions .
- Domain and range .
- Evaluating functions .
Applications :
- Stock market ; men in workforce .
Key Concepts :
* Data - Scatter plot – Inputs , Outputs - Function ( Graphically , Numerically , Analytically defined ) – Domain and Range - Functional Notation - The conditions of domains . 


LECTURE 

1.2            GRAPHS - MATHEMATICAL MODELS
Topics : 

- Graphing and evaluating functions with technology .
- Graphing and evaluating mathematical models .
Applications :
- Cost-Benefit , Bankruptcies .
Key Concepts :
* Point-Ploting methods – Graphing - Mathematical Models - Aligning Data - Evaluating functions with technology – Scatter Plots . 


LECTURE 

1.3             LINEAR FUNCTIONS 
Topics : 

- Linear functions .
- Intercepts and slopes .
- Constant rates of change .
Applications :
- Loan Balances , Temperature measurements .
Key concepts :
Linear functions – x and y-intercepts – Slope of the line - Linear Models - Slope-Intercept form – Rate of change – Special Functions .


LECTURE 

1.4             EQUATIONS OF LINES   
Topics : 
- Equations of lines .
- Constant and average rates of change .
Applications :

- Depreciation , Toyota sales .
Key concepts :
Equations of Lines – Slope-intercept form   - General form – Point -Slope form - Linear Models - Constant Rates of change – Average Rates of change  .


LECTURE 

1.5             SOLUTIONS OF LINEAR EQUATIONS   

Topics : 
- Solutions , zeros and x-intercept .
- Solving linear equations .
- Functional forms of equations in two variables .
Applications :
- Credit card debt , Simple interest .
Key concepts :
Solution of linear equations algebraically – graphically  – Solution of equations for a specified linear variable  .


LECTURE  

1.6            FITTING LINES  -  MODELING LINEAR FUNCTIONS  

Topics : 

- Linear Regression .
- Modeling and applying with linear equations .

 
Applications :

- SAT score , Health Service  .
Key concepts :
Fitting lines to data points – Linear Regression ( Least squares method ) – Applying Models  – Constant first Difference .



LECTURE  

1.7             MODELS IN BUSINESS AND ECONOMICS  

Topics : 
- Modeling Revenue , Cost and Profit .
- Break Even – Marginal Revenue , Cost and Profit , Supply and Demand .
- Market Equilibrium   .

 
Applications :
- Break Even in Production and Sales , Marginal Revenue and Cost , Market Equilibrium .

 
Key concepts :
Total Revenue – Total Cost – Profit – Marginal Profit – Marginal Revenue – Marginal Cost – Break Even


LECTURE  

1.8             SOLUTIONS OF LINEAR INEQUALITIES    

Topics : 
- Solving linear inequalities .
- Solving double (system) inequalities .

 
Applications :
- Profit , Body temperature .

 
Key concepts :
Linear inequalities – Algebraic solution of an inequality – Graphical solution of an inequality  - Double Inequalities .




LECTURE  
 
2.1            QUADRATIC FUNCTIONS , PARABOLAS 
 
Topics : 
 
- Quadratic function.
- Vertex of Parabola .
- Zero of Quadratic function .
 
Applications :
- Maximum revenue from sales .
 
Key Concepts :
*Quadratic function – Parabola – Zero of Quadratic function. 
 

LECTURE  
 
 2.2   QUADRATIC EQUATIONS  
 
Topics : 
 
- Solving Quadratic equations by algebraic method .
- Solving Quadratic equations by graphic method .
 
Applications :
- Profit , Break-Even .
 
Key Concepts :
* Solving Quadratic equations by graphic – algebraic method .
 


LECTURE  
 
2.3   POWER FUNCTIONS AND TRANSFORMATIONS 
 
Topics : 
 
- Power functions and root functions .
- Increasing and decreasing functions .
- Symmetry .
- Transformations of graphs .
 
Applications :
- Magnetude of stimulus and response .
- Mutual funds .
 
Key Concepts :
* Power functions –Increasing and decreasing – Root functions – Transformations ( Shift , Compression , Stretch , Reflection )
- Radical equations  .
 
 
LECTURE
 
2.4   QUADRATIC AND POWER MODELS 
 
Topics : 
 
- Quadratic functions.
- Comparing linear and quadratic models .
- Modeling with power functions .
- Comparing quadratic and power models.
 
Applications :
- Auto noise .
- Voting .
 
Key Concepts :
* Modeling quadratic functions - power functions – Comparison of models – First and second differences - Comparison of quadratic and power models
 
LECTURE  
 
2.5 RECIPROCAL , ABSOLUTE VALUE – PIECEWISE -DEFINED FUNCTIONS  
 
Topics : 
 
- Reciprocal functions .
- Absolute value and Piecewise-defined functions .
 
 
Applications :
- Cost - Benefit .
- Average cost .
- Residental power cost .
 
Key Concepts :
* Reciprocal functions – Average cost function – Piecewise-defined functions – Absolute value functions – Solving absolute value equations.
 
LECTURE  
 
2.6   INVERSE FUNCTIONS   
 
Topics : 
 
- Inverse functions.
- Finding and graphing the inverse of a functions .
 
 
Applications :
- Loan balances   .
- Money conversion .
 
Key Concepts :
* Inverse functions – Horizontal line test – Finding the inverse functions – Graphs of inverse functions.
 
LECTURE  
 
2.7   QUADRATIC AND POWER INEQUALITIES   
 
Topics : 
 
- Solving quadratic inequalities analytically and graphically .
- Solving power inequalities .
 
Applications :
- Internet users .
- Investment.
 
Key Concepts :
* Quadratic inequalities - Solving analytically –graphically – Power inequalities .
 

 
LECTURE  

3.1   EXPONENTIAL FUNCTIONS  

Topics : 
- Exponential functions . 
- Growth and decay .
- Transformation of graphs .
- Spreadsheet and the number e .

 
Applications :

- Federal funds.
- Sales decay .
Key Concepts :
* Exponential growth function – Horizontal asymptote – Transformation of graphs of exponential functions – The number e .



LECTURE  

3.2   LOGARITHMIC FUNCTIONS

Topics : 
- Logarithmic functions . 
- Common and natural logarithms .
- Change of base .
Applications :

- Richter scale .
- Doubling time for investments .

 
Key Concepts :
* Logarithmic functions – Base – logarithm – Exponent - Exponential and logarithmic forms - Common and natural logarithms - Change of base .  


 
LECTURE  

3.3   EXPONENTIAL EQUATIONS – PROPERTIES OF LOGARITHMS


Topics : 

- Logarithmic properties .
- Solving exponential and logarithmic equations . 
- Exponential inequalities .

 
Applications :
- Measuring earthquake intensity .
-Sales decay .
Key Concepts :
* Solving exponential equations–Properties of Logarithms .   



 
LECTURE  


3.4   EXPONENTIAL AND LOGARITHMIC MODELS  

Topics : 

- Modeling with exponential equations .
- Exponential and Logarithmic models .
- Comparison of models .

 
Applications :

-Sales decay .
- Inflation .
Key Concepts :

* Modeling with exponential equations – Comparing quadratic and exponential models - Logarithmic modeling .  


LECTURE 

3.5   EXPONENTIAL FUNCTIONS AND INVESTING  

Topics : 

- Compound interest .
- Continuous compounding . 
- Present value .
- Investment models .

 
Applications :

-Future value of an account .
- Continuous compounding .
- Present value of an investment .
- Mutual fund growth .

 
Key Concepts :
* Future value of investment – Interest compounded annually – Interest compounded k-times per year - Interest compounded continuous - Present value of an investment – Investment models .  


LECTURE  


3.6  ANNUITIES – LOAN REPAYMENT  


Topics : 
- Future value and Present value of an annuity .
- Amortization .
Applications :
- Future value of an ordinary annuity .
- Present value of an ordinary annuity .
- Home Mortage .
- Loan Repayment .
Key Concepts :
* Annuity – Ordinary Annuity – Present value of an investment - Present value of an ordinary annuity - Loan Repayment – Amortization .  


LECTURE 

3.7    LOGISTIC AND GOMPERTZ FUNCTIONS     

Topics : 

- Logistic growth and decay functions .
- Gompertz functions .

 
Applications :

- Company growth .
Key Concepts :
* Logistic functions  – Limiting value of logistic functions – Modeling logistic functions – Gompertz functions .  
 



LECTURE 
 
4.1    POLYNOMIAL FUNCTIONS   
 
Topics : 
 
- Polynomial functions .
- Cubic functions . 
- Quartic functions .
 
 
Applications :
- United Nations debt .
- Foreign born population .
 
 
Key Concepts :
* Polynomial functions –Cubic functions - Quartic functions – Local extrema ( local minimum , local maximum , absolute minimum, absolute maximum – Increasing and decreasing functions .  
 

LECTURE 
 
4.2    CUBIC AND QUARTIC FUNCTIONS     
 
Topics : 
 
- Modeling with cubic and quartic functions .
- Model comparison .
 
 
Applications :
- Sales of tobacco .
- US foreign born population .
 
Key Concepts :
*Cubic models – Quartic models .
 
LECTURE 
 
4.3     POLYNOMIAL EQUATIONS     
 
Topics : 
 
- Solving polynomial equations .
- Estimating solutions with technology .
 
Applications :
- Cost .
- FV of an investment .
- Stock prices .
 
Key Concepts :
* Solving polynomial equations – Estimating solutions with technology . 
 

LECTURE 
 
4.4                 SOLUTIONS OF POLYNOMIAL EQUATIONS 
 
Topics : 
 
 
- Solving cubic and quartic equations .
- Combining graphical and analytical methods .
 
Applications :
- Break-even revenue .
 
Key Concepts :
* Polynomial division – Using division to solve cubic equations – Combining graphical and analytical methods – Solving quartic equations . 
 
LECTURE
 
4.5                 COMPLEX SOLUTIONS -  FUNDAMENTAL THEOREM   OF ALGEBRA  
 
Topics : 
 
- Fundamental Theorem of Algebra .
- Imaginary and complex numbers .
- Operations with complex numbers .
- Quadratic and Polynomial equations with the complex solutions .
 
Applications :
- Fractal .
 
Key Concepts :
* Imaginary and complex numbers – Operation with complex numbers – Quadratic equations with the complex solutions – Polynomial equations with complex solutions – Fundamental Theorem of Algebra . 
 
 
LECTURE
 
4.6            RATIONAL FUNCTIONS AND RATIONAL EQUATIONS
         
Topics : 
 
- Rational functions .
- Solutions of rational equations .
 
Applications :

- Average cost of production .
- Cost - Benefit .
- Advertising and Sales .
 
Key Concepts :
* Graph of rational functions – Vertical asymptotes – Horizontal asymptotes – Slant asymptotes – Solving the rational equations ( analytically and graphically ) . 
 
LECTURE
 
4.7            POLYNOMIAL AND RATIONAL INEQUALITIES .
         
Topics : 
 
- Polynomial inequalities .
- Rational inequalities .
 
Applications :
- Average cost of production .
 
Key Concepts :
* Polynomial inequalities ( graphical solutions , analytical solutions )– Rational inequalities ( graphical solutions , analytical solutions )   .
 


LECTURE 
 
5.1            SYSTEMS OF LINEAR EQUATIONS IN 2 VARIABLES
         
Topics : 
 
- Graphical solution of systems .
- Modeling systems of linear equations .
- Inconsistent and dependent systems .
 
Applications :
- Break-even .
- Market equilibrium .
- Investing .
 
Key Concepts :
* Solution of systems of equations ( by graphing , substitution , elimination )– Type of systems ( unique solutions , dependent systems , inconsistent systems ) – Market equilibrium ( demand , supply ) – Modeling systems of linear equations .
 
 
LECTURE 
 
5.2            SYSTEMS OF LINEAR EQUATIONS IN 3 VARIABLES - MATRIX SOLUTION 
         
Topics : 
 
- Left-to-right elimination method .
- Matrix representation of systems of linear equations .
- Solving systems with matrices.
- Gauss-Jordan elimination method .
 
 
Applications :
- Product transportation .
- Manufacturing .
- Investment .
 
Key Concepts :
* Left-to-right elimination method – Matrix representation of systems of linear equations ( matrix , dimensions , square matrix , indentity matrix , augmented matrix , coefficient matrix ) – Gauss-Jordan elimination method – Solution with technology .
 
 
LECTURE 
 
5.3            SYSTEMS OF LINEAR EQUATIONS WITH NON-UNIQUE SOLUTIONS 
         
Topics : 
 
- Non-unique solutions .
- Dependent systems of linear equations .
- Inconsistent systems .
 
Applications :

- Purchashing .
- Investment .
- Transportation .
 
Key Concepts :
* Non-unique solutions – Dependent systems – Inconsistent systems  .
 
 
LECTURE 
 
5.4            MATRICES – BASIC OPERATIONS 
         
Topics : 
 
- Addition and substraction of matrices .
- Multiplication of a matrix by a number   .
- Matrix multiplication .
- Multiplication with technology .
 
Applications :
- Pricing .
- Trade Balance .
- Advertising .
- Manufacturing .
 
Key Concepts :
* Matrix operations ( Addition , Substraction , Multiplication by a constant – Matrix multiplication ) .
 
LECTURE 
 
5.5            INVERSE MATRICES – MATRIX EQUATIONS 
         
Topics : 
 
- Inverse matrices .
- Inverse and technology   .
- Solving matrix equations .
- Matrix equations with technology .
 
Applications :
- Manufacturing .
- Investment .
 
 
Key Concepts :
Inverse matrices - Inverse and technology - Solving matrix equations .
 


LECTURE 
 
6.1              SYSTEMS OF LINEAR INEQUALITIES 
         
Topics : 
 
- Linear inequalities in 2 variables .
- Systems of linear inequalities in 2 variables .
 
Applications :
- Auto purchases .
- Car rental .
- Advertising .
 
Key Concepts :
* Linear inequalities in 2 variables ( Solution region , test point ) – Systems of linear inequalities in 2 variables ( border , corner ) .
 
 
 
LECTURE 
 
6.2 LINEAR PROGRAMMING - GRAPHICAL METHODS 
         
Topics : 
 
- Linear programming .
- Solutions with technology .
 
Applications :

- Maximizing Car rental profit .
- Cost Minimization .
- Profit .
 
Key Concepts :
* Linear programming   – Constraints – Objective function – Feasible solution – Feasible region – Optimum value ( Maximum , minimum )  .
 
 
LECTURE 
 
6.3              SEQUENCES   - DISCRETE FUNCTIONS  
         
Topics : 
 
- Sequences .
- Arithmetic Sequences .
- Geometric Sequences .
 
Applications :

- Investment .
- Depreciation .
- Compound Interest .
 
Key Concepts :
* Sequences   – Arithmetic Sequences – Geometric Sequences   .
 
 
LECTURE 
 
6.4            SERIES  
         
Topics : 
 
- Finite and Infinite Series .
- Arithmetic and Geometric Series .
- Infinite Geometric Series
 
Applications :

- Profit .
- Depreciation .
- Annuities .
 
Key Concepts :
* Finite Series   – Infinite Series - Sigma Notation - Arithmetic Series – Geometric Series - Infinite Geometric Series   .
 
 
LECTURE 
 
6.5            PREPARING FOR CALCULUS  
         
Topics : 
 
- Simplifying expressions and fractions .
- Evaluating Functions .
- Rewriting Radical .
- Decomposition of Functions .
- Rewriting Expressions using negative and positive exponents .
- Using logarithmic properties .
- Reducing Fractions .
 
 
Applications :
 
- The equation of tangent line .
 
Key Concepts :
* Chapter 1 Skills    – Chapter 2 Skills – Chapter 3 Skills – Chapter 4 Skills – Chapter 5 Skills .
 



 
 

 
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