PACKAGE FOR 10 “CALCULUS TWO” 2-HOUR SESSIONS
Conquering Calculus 2!
We are offering a 10-session package designed to help students excel in their Calculus 2 courses, whether taken in high school as an advanced course or in college as a second-semester calculus class.
This program provides personalized instruction focused on mastering advanced integration techniques, series and sequences, and further applications of calculus.
Each session includes:
-A thorough review of lessons, homework, and exam materials
-Extra practice problems, including past exam-style questions
-Tailored strategies for improving problem-solving speed and accuracy
-Regular progress tracking with personalized feedback after every session
-Students will also build academic strategies such as effective study habits, time management during exams, and the best use of online and textbook resources.
Curriculum:
- 1. Techniques of IntegrationIntegration by parts
Trigonometric integrals
Trigonometric substitution
Partial fraction decomposition
Improper integrals (infinite intervals and discontinuous integrands) - 2. Applications of Definite IntegralsFinding area between curves
Volume of solids of revolution (disk, washer, and shell methods)
Arc length of curves
Surface area of solids of revolution
Work done by variable forces (springs, pumping fluids, etc.) - 3. Sequences and SeriesUnderstanding sequences and their limits
Infinite series and convergence
Tests for convergence (n-th term test, integral test, comparison tests, ratio and root tests, alternating series test)
Power series and intervals of convergence
Taylor series and Maclaurin series expansions - 4. Parametric Equations and Polar CoordinatesGraphing parametric curves
Calculating derivatives and areas for parametric curves
Polar coordinates: graphing polar curves, finding areas bounded by polar graphs - 5. Introduction to Differential EquationsSolving simple first-order differential equations (separable, linear)
Modeling physical situations with differential equations (e.g., exponential growth and decay)By the end of the program, students will have mastered the advanced techniques and concepts necessary for Calculus 2 success, both in coursework and in preparing for further advanced math studies.
Notes:
Calculus 2 = Sequences and Series are a huge part.
Techniques of integration are big and more complicated than Calc 1.
Parametric and polar topics are covered more deeply here than they are in Calc 1.
Differential equations here are slightly more advanced than in Calc 1 (but still first-order).
