MTH 263 Calculus I (4 cr.)
Presents concepts of limits, derivatives, differentiation of various types of functions and use of differentiation rules, application of differentiation, antiderivatives, and integrals. This course replaces MTH 173 or MTH 175 or MTH 273 and is the first course in a three-course sequence. Prerequisite: Placement into MTH 263 or completion of MTH 167 or MTH161/162 or equivalent with a grade of C or better. Lecture 4 hours per week.
Major Topics:
Limits
Derivatives and Differentiation Rules
Applications of Differentiation
Integrals
Objectives and Skills:
Differentiate between the limit and the value of a function at a point
Find the limit of a function by numerical and graphical methods
Find limit of a function by analytical methods
Apply Limit Laws
Calculate one-sided and two-sided limits of a function
Prove the existence of a limit using precise definition of the limit
Determine the continuity of a function
Calculate Vertical and Horizontal asymptotes using limits
Define Derivatives and Rates of Change
Compute derivatives of basic functions using the definition of the derivative
Differentiate polynomial, rational, radical, exponential and logarithmic functions
Find equation of a line tangent to graph of f(x) at the point (x, y) using derivative
Differentiate trigonometric functions
Apply product, quotient, chain rules
Apply implicit differentiation and find derivatives of inverse trigonometric functions
Apply concept of rates of change to natural and social sciences
Apply the concept of related rates
Define hyperbolic functions and their derivatives
Find linear approximation of a function at a given point
Calculate local and absolute maximum and minimum values of a function
Apply Rolle’s Theorem and Mean Value Theorem to study properties of a function
Find critical points and intervals of increase and decrease of a function
Find points of inflection and concavity intervals
Sketch a curve for a given function using derivatives
Apply rules of differentiation to solve optimization problems
Find antiderivatives for basic functions using knowledge of derivatives
Relate areas to definite integrals using sigma notation, Riemann Sums, and limits
Apply Fundamental Theorem of Calculus to find definite integrals and area under the graph of f(x)
Find indefinite integrals of polynomials and basic trigonometric and exponential function
Apply Net Change Theorem
Perform integration using substitution rule
Find areas between curves
Find average value of a function