M 161 Survey of Calculus
Prerequisite: M 121 or appropriate placement test score.
Covers basic calculus concepts including limits, differentiation, and integration with applications to business, science, and social science problems.
- Explain and apply the concept of limit, infinite limits, limits at infinity, asymptotes and how to solve limit problems involving rational and piece-wise defined functions;
- Explain the limit definition of the derivative of a function, how it relates to the function itself, and how to use it to compute derivatives in elementary cases;
- Explain and apply the power, sum, product, and quotient rules of differentiation;
- Explain and apply the derivative of exponential and logarithmic functions;
- Explain and apply implicit and logarithmic differentiation;
- Graphically analyze functions including how to find local and global extrema, concavity, and inflection points;
- Use the derivative to solve related rate and optimization word problems;
- Define the definite integral and how to estimate it for linear and quadratic functions;
- Explain antiderivatives and the Fundamental Theorem of Calculus;
- Use substitution and integration by parts to compute the integrals of polynomials, first-degree rational functions, and exponential functions;
- Find the area between the graphs of two functions.Understand linear functions, linear inequalities and apply them to solve real-world problems