
MTH 1110  Calculus I4 lecture hours 0 lab hours 4 credits Course Description This initial course in calculus introduces the concepts of limits, differentiation, and integration. Topics include limits, continuity, differentiation of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions, definite and indefinite integrals, Fundamental Theorem of Calculus, and method of substitution. Applications include graphing, extreme values, related rates, optimization, local linear approximation, Newton’s method, and rectilinear motion. Prereq: MTH 1080 or placement in MTH 1110 (quarter system prereq: MA 120 or placement into MTH 1110) Note: None This course meets the following Raider Core CLO Requirement: None Course Learning Outcomes Upon successful completion of this course, the student will be able to:
 Evaluate twosided and onesided limits graphically
 Identify vertical and horizontal asymptotes using limits
 Evaluate the limits of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric, and composite functions analytically
 Determine if a function is continuous at a point by analyzing the three conditions of continuity
 Identify removable, jump, and infinite discontinuities
 Interpret the derivative as instantaneous rate of change and slope of tangent line
 Find the derivative of a function using the limit definition
 Find an equation for a tangent line
 Analyze the behavior of the derivative from the graph of a function, including identifying points of nondifferentiability
 Find the derivative of algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions
 Determine the appropriate rules to use in differentiating various functions
 Apply basic differentiation rules including power, product, quotient, and chain rules to find derivatives
 Find higherorder derivatives
 Use various notations for derivatives
 Find and interpret the position, velocity, and acceleration of a moving object
 Find derivatives implicitly
 Find a derivative using logarithmic differentiation
 Solve related rates problems
 Find relative extrema using First and Second Derivative tests
 Find absolute extrema on closed, open, and infinite intervals
 Use derivatives to find points of inflection on a curve
 Solve optimization problems
 Use Newton’s method to approximate a zero of a function
 Find the differential of a function and use it to approximate error
 Find the local linear approximation of a function about a point
 Integrate functions involving algebraic, exponential, trigonometric, logarithmic, and inverse trigonometric forms
 Solve an initial value problem
 Evaluate a definite integral by the limit of Riemann sums
 Apply and interpret the Fundamental Theorem of Calculus Part I and Part II
 Evaluate definite integrals by Fundamental Theorem of Calculus
 Evaluate indefinite and definite integrals using the method of substitution
 Find position and velocity functions using integration
 Find displacement and distance traveled using integration
Prerequisites by Topic Course Topics
 Limits and continuity
 Rates of change, tangent lines, and the definition of derivative
 Derivatives of algebraic, trigonometric, exponential, logarithmic, inverse trigonometric, and composite functions
 Related rates problems
 First and second derivative tests for extrema, curve sketching
 Optimization problems
 Mean Value Theorem
 Newton’s method
 Local linear approximation and differentials
 Definite and indefinite integrals
 Fundamental Theorem of Calculus, Part I and Part II
 Integration by method of substitution
 Rectilinear motion
Coordinator Dr. Niles Armstrong
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