MA1113 Single Variable Calculus I

Review of analytic geometry and trigonometry, functions of one variable, limits, derivatives, continuity and differentiability; differentiation of algebraic, trigonometric, logarithmic and exponential functions with applications to maxima and minima, rates, differentials; product rule, quotient rule, chain rule; anti-derivatives, integrals and the fundamental theorem of calculus; definite integrals, areas. Taught at the rate of nine hours per week for five weeks. Prerequisites: None.

Lecture Hours

4

Lab Hours

1

Course Learning Outcomes

• Define and explain the concept of a limit, evaluate limits of functions, including indeterminate forms and use the limit definition to determine if a function is continuous.

• State the limit definition of the derivative and use it to calculate derivatives of basic functions.

• Apply differentiation rules to calculate the derivatives of rational, trigonometric, inverse-trigonometric, exponential, and logarithmic functions as well as composite (Chain Rule) and implicit functions.
• Approximate functions near a value using linear approximations and differentials.

• Use derivatives to identify local and global extrema (maxima and minima) and use the second derivative to describe the concavity and inflection points of functions.

• Formulate and solve real-world optimization and related rates problems involving differential calculus in fields such as physics, economics, and biology.
• Define and compute antiderivatives (as the inverse process of differentiation) and definite integrals (as limits of Riemann sums) and connect the two concepts by applying the Fundamental Theorem of Calculus.