2. Discrete Time Models, Sequences, and Difference Equations.
Exponential Growth and Decay. Sequences. More Population Models. Review Problems.
3. Limits and Continuity.
Limits. Continuity. Limits at Infinity. The Sandwich Theorem and Some Trigonometric Limits. Properties of Continuous Functions. Formal Definition of Limits. Review Problems.
Formal Definition of the Derivative. The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials. Product Rule and Quotient Rule. The Chain Rule and Higher Derivatives. Derivatives of Trigonometric Functions. Derivatives of Exponential Functions. Derivatives of Inverse and Logarithmic Functions. Approximation and Local Linearity. Review Problems.
5. Applications of Differentiation.
Extrema and the Mean Value Theorem. Monotonicity and Concavity. Extrema, Inflection Points and Graphing. Optimization. L'Hopital's Rule. Difference Equations - Stability. Numerical Methods: The Newton-Raphson Method. Antiderivatives. Review Problems.
The Definite Integral. The Fundamental Theorem of Calculus. Applications of Integration. Review Problems.
7. Integration Techniques and Computational Methods.
The Substitution Rule. Integration by Parts. Practicing Integration and Partial Fractions. Improper Integrals. Numerical Integration. Tables of Integration. The Taylor Approximation. Review Problems.
8. Differential Equations.
Solving Differential Equations. Equilibria and Their Stability. Systems of Autonomous Equations. Review Problems.
9. Linear Algebra and Analytic Geometry.
Linear Systems. Matrices. Linear Maps, Eigenvectors and Eignvalues. Analytic Geometry. Review Problems.
10. Multivariable Calculus.
Functions of Two or More Independent Variables. Limits and Continuity. Partial Derivatives. Tangent Planes, Differentiability, and Linearization. More About Derivatives. Applications. Systems of Difference Equations. Review Problems.
11. Systems of Differential Equations.
Linear Systems: Theory. Linear Systems: Applications. Nonlinear Autonomous Systems: Theory. Nonlinear Systems: Applications. Review Problems.
12. Probability and Statistics.
Counting. What Is Probability? Conditional Probability and Independence. Discrete Random Variables and Discrete Distributions. Continuous Distributions. Limit Theorems. Statistical Tools. Review Problems.
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