Apply Newton’s method to approximate solutions to equations.Use L’Hopital’s Rule to evaluate limits involving indeterminate forms.Use the tools of calculus and algebra to sketch, by hand, good graphs of functions including intercepts, critical points, inflection points, and asymptotes.Apply the first and second derivative tests to classify critical points. Use the first and second derivatives of a function to identify where a function is increasing or decreasing, concave up or concave down. Identify the candidates for the extreme values of a function and give the extreme values of a function.Apply linearization of a function at a point to calculate approximations use differentials to estimate errors.Apply logarithmic differentiation to find derivatives.Differentiate inverse functions, including logarithmic functions and inverse trigonometric functions.Apply the chain rule to differentiate implicitly-defined functions and related rates problems.Relate differentiation to rates of change, including position, velocity, and acceleration.Know and apply the rules for differentiation (power, exponential, trigonometric, sum, product, quotient, chain).Find tangent lines to functions and interpret a tangent line geometrically as a local approximation to the function.Recognize and use the various symbols for derivatives. Compute higher order derivatives and include units. Use the limit definition of derivative to calculate the derivative of relatively simple functions. Give the limit definition of derivative at a point.Use limits to identify and classify discontinuities. Demonstrate how to identify continuous functions. The demonstration of understanding should occur without applying L’Hopital’s Rule. Demonstrate understanding of limits, including how to evaluate limits, one-sided limits, limits involving $\frac$ as $\theta\to0$, and limits involving infinity.Given a function and an interval or a point, find average rate of change, calculate instantaneous rate of change, and relate both to the graph of the function.Students should access the online homework (MyMathLab) only through Canvas.īasics of differentiation (Sections 2.1, 2.2, 2.4-2.6, 3.1 – 3.6) includes discussion of average rates of change, limits, the definition of derivative, and differentiation rules.Īdvanced differentiation (Sections 3.7 – 3.11, 4.1 – 4.4, 4.6) includes discussion of implicit differentiation, logarithmic differentiation, derivatives of inverse functions, related rates, linearization, optimization, and curve sketching.īasics of integration (Sections 4.5, 4.7, 4.8, 5.1 – 5.6, 7.1 – 7.3) includes antiderivatives, finite sums, definite integrals, the Fundamental Theorem of Calculus, separable differential equations, and hyperbolic functions.Īfter completing Math 165, students should be able to: The access code provides access to the online homework package. Weir and Joel Hass accompanies a purchased access code. The etext version of Pearson’s textbook Thomas’ Calculus, Early Transcendentals, 14th Edition, by George Thomas, Jr., Maurice D. Applications of differentiation, including optimization, are explored. Prerequisite : Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry or minimum of C- in MATH 143īasic Calculus provides an introduction to differential and integral calculus. Differential calculus, applications of the derivative, introduction to integral calculus.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |