
Advance to the second part of calculus by exploring further integration techniques and series, take notes, complete practice questions, and build long-term memory.
Learn to compute volumes with the shell method, slicing parallel to the rotation axis, using circumference and height, with y axis rotation examples.
Master solving trigonometric integrals by applying common identities, recognizing tangent and secant shortcuts, and using substitution for odd/even power cases.
Explore improper integrals by turning infinite bounds into limits, handling discontinuities and domain checks, and testing convergence or divergence while carrying the limit to the end.
Explore the application of integrals to continuous probability distributions, including the exponential distribution for waiting times, and compute mean and median using density functions and area constraints.
Explore sequences in calculus two, including sequence notation and formulas, domain natural numbers, limit laws, and L'Hôpital's rule, to determine convergence or divergence with practical examples.
Use the ratio test by substituting n+1 for n and taking the limit of a_{n+1}/a_n in absolute value: if < 1, converges; if > 1, diverges; if = 1, inconclusive.
Are you struggling with calculus or feeling overwhelmed by complicated formulas? You’re not alone! This course is designed to make calculus approachable, practical, and even enjoyable, with no memorization required.
What Makes This Course Different?
Fundamental Understanding: Learn how to solve calculus problems from the ground up, focusing on intuition and understanding rather than rote memorization.
Concise & Comprehensive: Each lecture is packed with essential knowledge and helpful tips, ranging from just 5 to 30 minute, perfect for busy learners.
Step-by-Step Solutions: I walk you through every problem, breaking down complex concepts into manageable steps.
Complete Resources: Access detailed class notes, fully worked solutions, and blank homework questions under each video to reinforce your learning and practice your skills.
What You Will Learn
Integration Techniques:
Master advanced integration methods, including integration by parts, trigonometric substitution, partial fractions, and strategies for integrating trigonometric, exponential, and logarithmic functions.
Applications of Integration:
Discover how integration is used in real-world contexts such as physics, probability, and economics. Learn to calculate areas, volumes, arc lengths, and surface areas of various shapes.
Sequences and Series:
Understand the fundamentals of sequences and series, including convergence tests, Taylor and Maclaurin series, and power series representations. Gain the skills to analyze and manipulate these powerful mathematical tools.
Who Is This Course For?
High school and college students taking calculus
Anyone preparing for AP Calculus, university exams, or standardized tests
Lifelong learners seeking a deeper understanding of calculus concepts
Take the stress out of calculus and build real problem-solving confidence. Enroll now and let’s master calculus together one step at a time!