## Mathematics

### University e-Preparation Course

1 FUNDAMENTALS OF ALGEBRA.
1.1 Real Numbers

1.2 Polynomials

1.3 Factoring Polynomials

1.4 Rational Expressions

1.5 Integral Exponents

1.6 Solving Equations

1.9 Inequalities and Absolute Value.

2 FUNCTIONS AND THEIR GRAPHS.
2.1 The Cartesian Coordinate System and Straight Lines

2.2 Equations of Lines

2.3 Functions and Their Graphs

2.4 The Algebra of Functions

2.5 Linear Functions

2.7 Functions and Mathematical Models

2.8 The Method of Least Squares.

3 EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
3.1 Exponential Functions

3.2 Logarithmic Functions

3.3 Exponential Functions as Mathematical Models.

4 MATHEMATICS OF FINANCE.
4.1 Compound Interest

4.2 Annuities

4.3 Amortization and Sinking Funds

4.4 Arithmetic and Geometric Progressions.

5 SYSTEMS OF LINEAR EQUATIONS AND MATRICES.
5.1 Systems of Linear Equations: An Introduction

5.2 Systems of Linear Equations: Unique Solutions

5.3 Systems of Linear Equations: Underdetermined.and Overdetermined Systems

5.4 Matrices

5.5 Multiplication of Matrices

5.6 The Inverse of a Square Matrix.

6 LINEAR PROGRAMMING.
6.1 Graphing Systems of Linear Inequalities in Two Variables

6.2 Linear Programming Problems

6.3 Graphical Solution of Linear Programming Problems

6.4 The Simplex Method: Standard Maximization Problems

6.5 The Simplex Method: Standard Minimization Problems.

7 SETS AND PROBABILITY.
7.1 Sets and Set Operations

7.2 The Number of Elements in a Finite Set

7.3 The Multiplication Principle

7.4 Permutations and Combinations

7.5 Experiments, Sample Spaces, and Events

7.6 Definition of Probability

7.7 Rules of Probability.

8.1 Use of Counting Techniques in Probability

8.2 Conditional Probability and Independent Events

8.3 Bayes’ Theorem

8.4 Distributions of Random Variables

8.5 Expected Value

8.6 Variance and Standard Deviation.

9 THE DERIVATIVE.
9.1 Limits

9.2 One-Sided Limits and Continuity

9.3 The Derivative

9.4 Basic Rules of Differentiation

9.5 The Product and Quotient Rules Higher Order Derivatives

9.6 The Chain Rule

9.7 Differentiation of Exponential and Logarithmic Functions

9.8 Marginal Functions in Economics.

10 APPLICATIONS OF THE DERIVATIVE.
10.1 Applications of the First Derivative

10.2 Applications of the Second Derivative

10.3 Curve Sketching

10.4 Optimization I

10.5 Optimization II.

11 INTEGRATION.
11.1 Antiderivatives and the Rules of Integration

11.2 Integration by Substitution

11.3 Area and the Definite Integral

11.4 The Fundamental Theorem of Calculus

11.5 Evaluating Definite Integrals

11.6 Area between Two Curves

11.7 Applications of the Definite Integral to Business and Economics.

12 CALCULUS OF SEVERAL VARIABLES.
12.1 Functions of Several Variables

12.2 Partial Derivatives

12.3 Maxima and Minima of Functions of Several Variables.

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