MATH 1070 - Survey of Calculus

1. Applications of the Derivative including Maxima and Minima
2. Differentiation The derivative Derivatives of algebraic and composite functions Derivatives of higher order
3. Exponential and Logarithmic Functions Differentiation of exponential and logarithmic functions Integration of exponential and logarithmic functions
4. Functions of Two Variables Partial derivatives Relative extrema Applied problems on maxima and minima
5. Functions, Graphs and Limits
6. Integration The definite integral The fundamental theorem of integral calculus Evaluating integrals Applications
7. Techniques of Integration Substitution–change of variable Integration by parts Integration tables

1. Demonstrate critical and logical reasoning when solving problems.
2. Determine the derivative of a function graphically, numerically, and symbolically.
3. Find the derivative of algebraic and composite functions symbolically.
4. Find higher order derivatives.
5. Solve an optimization application problem by using the derivative.
6. Determine the integral of a function graphically, numerically, and symbolically.
7. Differentiate and integrate exponential and logarithmic functions
8. Communicate clearly a problems solution and its explanation for the intended audience in terms of the problem posed.
9. Determine an integral by using techniques such as substitution, integration by parts, and integration tables.
10. Find maxima and minima for functions of two variables.
11. Find partial derivative for functions of two variables.
12. Find relative extrema for functions of two variables.
13. Model and solve physics and other various application problems by applying and evaluating an integral.

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