Exploratory projects in Calculus with Early Transcendentals immerse students in challenging, real-world applications of course material. Assign these projects as homework or small group assignments to stimulate discussion and collaboration among your class. In light of the recent SpaceX launch to the International Space Station, consider assigning this project, in which velocity, acceleration, and Newton’s … Continue reading Calculus with Out-of-This-World Applications
Calculus with Early Transcendentals
Answer Equivalence in Calculus Courseware
We know that oftentimes in calculus, there's more than one way to solve a problem. While some online systems don't allow for multiple correct answers, Hawkes Learning's courseware was built by subject matter experts who painstakingly went through examples to ensure students are given credit for equivalent answers. Marvin, one of our lead calculus content … Continue reading Answer Equivalence in Calculus Courseware
Inside Our Calculus Courseware: Trigonometric Integrals
Trigonometric functions are inherently tricky to deal with. There are so many identities and equivalent forms, students are often paralyzed before they start. Our Tutor screens are student-friendly and skillfully guide them through this trigonometric maze. Sample Problem #1 In the following problem, the student must recognize that the parity (odd or even) of an … Continue reading Inside Our Calculus Courseware: Trigonometric Integrals
Inside Our Calculus Courseware: Trigonometric Substitutions
The word “Trigonometric” by itself scares students. Combining it with “Substitutions and Evaluation” is downright terrifying. After all, the student must select the appropriate substitution, transform the integrand from an algebraic to a trigonometric expression, make the appropriate change in limits of integration (or rewrite their antiderivative in terms of the original variable), and finally … Continue reading Inside Our Calculus Courseware: Trigonometric Substitutions
Inside Our Calculus Courseware: Convergence Tests
The sheer amount of convergence tests can overwhelm students. Our courseware breaks down the information for students and provides error-specific feedback through the Explain Error tool. Explain Error is available in the Practice mode to anticipate and diagnose common errors. When a student makes a mistake, the courseware shows them specifically where and how they … Continue reading Inside Our Calculus Courseware: Convergence Tests
Inside Our Calculus Courseware: Integration by Parts
The integration by parts method is not straightforward. It requires some thought, and the student must make two initial choices. Successfully working the exercises demands these choices be wise ones. And it may be necessary to repeat the process. Students often think they’ve failed if one application doesn’t yield the solution. Sample Problem #1 Below … Continue reading Inside Our Calculus Courseware: Integration by Parts
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