Course Description for MTH1123 Calculus for Engineers I

Student Population: First year engineering and computer science students (some architecture, math and science majors)

Note: There are several versions of this course:

• MTH1120 is for students who would profit from a greater depth of coverage at a slower pace (including some pre-calculus review)
• MTH1140 is for mathematics and science majors and is effectively interchangeable with MTH1123
• MTH1723 and MTH1740 are the honors versions of 1123 and 1140.

Goals: The concept of rate-of-change and instantaneous rate-of-change (derivative) is fundamental to most physical processes. The goals of this course are to understand the concept of the derivative, to develop the techniques of computing derivatives, and to learn how the derivative can be used in mathematical modeling and problem-solving. Calculators and computers will be used frequently to enhance visualization and numerical calculations. Early emphasis is placed on the linear, trigonometric and exponential functions.

Topics:

• Functions and rates of change of functions: algebraic, exponential/logarithmic and trigonometric
• The derivative as a limit of rates of change
• Graphical significance of the derivative and the second derivative
• Rules for differentiation of sums, products, quotients and composite functions
• Derivatives of rational functions, exponential/logarithmic and trigonometric/inverse trigonometric functions.
• Linear approximations and Newton's method
• Applications to velocity/acceleration, growth and decay and optimization.
• Computer lab problem sets on linearization, Newton's method, Curve-sketching, and other selected s.