{"id":11249,"date":"2026-07-09T14:27:36","date_gmt":"2026-07-09T14:27:36","guid":{"rendered":"https:\/\/www.myengineeringbuddy.com\/blog\/calculus-1-2-topics-for-online-tutoring\/"},"modified":"2026-07-12T04:24:01","modified_gmt":"2026-07-12T04:24:01","slug":"calculus-1-2-topics-for-online-tutoring","status":"publish","type":"post","link":"https:\/\/www.myengineeringbuddy.com\/blog\/calculus-1-2-topics-for-online-tutoring\/","title":{"rendered":"Calculus 1 and 2 Topics: A Complete Course Overview"},"content":{"rendered":"\n<div style=\"background-color:#f8f8f8; border-left:4px solid #d0d0d0; padding:12px 16px; margin-bottom:20px;\"><strong>Key Takeaways<\/strong>\n<ul>\n<li>Calculus is divided into Calculus 1, Calculus 2, and Calculus 3 (Multivariable).<\/li>\n<li>Calculus 1 covers limits, derivatives, integrals, and differential equations.<\/li>\n<li>Calculus 2 extends integration techniques, series, and parametric equations.<\/li>\n<li>Both courses share foundational integral and differential equation topics.<\/li>\n<li>Wikipedia maintains a complete list of calculus topics across all levels.<\/li>\n<\/ul><\/div>\n\n<p>Calculus is basically divided into Calculus 1 and Calculus 2. Calculus 3 is three-dimensional calculus and also called <strong>Multivariable Calculus<\/strong> (we have not covered Calculus 3 topics in this post). If you need a <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/calculus\/\">calculus tutor<\/a>, the topics below outline exactly what each course covers.<\/p>\n\n<h2>Calculus 1 Topics<\/h2>\n\n<p>Calculus 1 builds the foundation of the subject, beginning with limits and continuity before moving into derivatives and their applications. Students working through <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/ap-calculus\/\">AP Calculus<\/a> will recognise most of these topics as core curriculum. The full topic list for Calculus 1 is below.<\/p>\n\n<h3>Limits and Continuity<\/h3>\n<ul>\n<li>Limits and continuity<\/li>\n<li>Estimating limits from tables<\/li>\n<li>Estimating limits from graphs<\/li>\n<li>Formal definition of limits (epsilon-delta)<\/li>\n<li>Properties of limits<\/li>\n<li>Limits using algebraic manipulation<\/li>\n<li>Limits by direct substitution<\/li>\n<li>Strategy in finding limits<\/li>\n<li>Squeeze theorem<\/li>\n<li>Continuity at a point<\/li>\n<li>Continuity over an interval<\/li>\n<li>Types of discontinuities<\/li>\n<li>Removing discontinuities<\/li>\n<li>Limits at infinity<\/li>\n<li>Infinite limits<\/li>\n<li>Intermediate value theorem<\/li>\n<\/ul>\n\n<h3>Derivatives: Definition and Basic Rules<\/h3>\n<ul>\n<li>Average vs. instantaneous rate of change<\/li>\n<li>Secant lines<\/li>\n<li>Estimating derivatives<\/li>\n<li>Differentiability<\/li>\n<li>Power rule<\/li>\n<li>Combining the power rule with other derivative rules<\/li>\n<li>Derivatives of cos(x), sin(x), e\u02e3, and ln(x)<\/li>\n<li>Product rule<\/li>\n<li>Quotient rule<\/li>\n<\/ul>\n\n<h3>Derivatives: Chain Rule and Advanced Topics<\/h3>\n<ul>\n<li>Implicit differentiation<\/li>\n<li>Differentiating inverse functions<\/li>\n<li>Derivatives of inverse trigonometric functions<\/li>\n<li>Strategy in differentiating functions<\/li>\n<li>Differentiation using multiple rules<\/li>\n<li>Second derivatives<\/li>\n<li>Disguised derivatives<\/li>\n<li>Logarithmic differentiation<\/li>\n<\/ul>\n\n<h3>Applications of Derivatives<\/h3>\n<ul>\n<li>Meaning of the derivative in context<\/li>\n<li>Straight-line motion<\/li>\n<li>Non-motion applications of derivatives<\/li>\n<li>Introduction to related rates<\/li>\n<li>Solving related rates problems<\/li>\n<li>Approximation with local linearity<\/li>\n<li>L&#8217;H\u00f4pital&#8217;s rule<\/li>\n<li>L&#8217;H\u00f4pital&#8217;s rule: composite exponential functions<\/li>\n<\/ul>\n\n<h3>Analyzing Functions<\/h3>\n<ul>\n<li>Mean value theorem<\/li>\n<li>Extreme value theorem and critical points<\/li>\n<li>Relative (local) extrema<\/li>\n<li>Absolute (global) extrema<\/li>\n<li>Concavity and inflection points intro<\/li>\n<li>Analyzing concavity and inflection points<\/li>\n<li>Second derivative test<\/li>\n<li>Sketching curves<\/li>\n<li>Connecting f, f&#8217;, and f&#8221;<\/li>\n<li>Solving optimization problems<\/li>\n<li>Analyzing implicit relations<\/li>\n<\/ul>\n\n<h3>Integrals<\/h3>\n\n<p>For students also studying statistics alongside calculus, this <a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/find-a-great-online-statistics-tutor-the-complete-guide-to-mastering-statistical-thinking\/\">guide to mastering statistical thinking<\/a> covers complementary mathematical reasoning skills.<\/p>\n\n<ul>\n<li>Accumulations of change<\/li>\n<li>Approximation with Riemann sums<\/li>\n<li>Summation notation review<\/li>\n<li>Riemann sums in summation notation<\/li>\n<li>Defining integrals with Riemann sums<\/li>\n<li>Fundamental theorem of calculus and accumulation functions<\/li>\n<li>Interpreting the behavior of accumulation functions<\/li>\n<li>Properties of definite integrals<\/li>\n<li>Fundamental theorem of calculus and definite integrals<\/li>\n<li>Reverse power rules<\/li>\n<li>Indefinite integrals of common functions<\/li>\n<li>Definite integrals of common functions<\/li>\n<li>Integrating with u-substitution<\/li>\n<li>Integrating using long division and completing the square<\/li>\n<li>Integrating using trigonometric identities<\/li>\n<\/ul>\n\n<h3>Differential Equations (Calculus 1)<\/h3>\n<ul>\n<li>Verifying solutions for differential equations<\/li>\n<li>Sketching slope fields<\/li>\n<li>Reasoning using slope fields<\/li>\n<li>Separation of variables<\/li>\n<li>Particular solutions to differential equations<\/li>\n<li>Exponential models<\/li>\n<\/ul>\n\n<h3>Applications of Integrals (Calculus 1)<\/h3>\n<ul>\n<li>Average value of a function<\/li>\n<li>Straight-line motion<\/li>\n<li>Non-motion applications of integrals<\/li>\n<li>Area: vertical area between curves<\/li>\n<li>Area: horizontal area between curves<\/li>\n<li>Area: curves that intersect at more than two points<\/li>\n<li>Volume: triangles and semicircles cross-sections<\/li>\n<li>Volume: squares and rectangles cross-sections<\/li>\n<li>Volume: disc method (revolving around x- and y-axes)<\/li>\n<li>Volume: disc method (revolving around other axes)<\/li>\n<li>Volume: washer method (revolving around x- and y-axes)<\/li>\n<li>Volume: washer method (revolving around other axes)<\/li>\n<\/ul>\n\n<p>Engineering students will find the <a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/engineering-mathematics-survival-kit-ai-assisted-learning-strategies\/\">engineering mathematics survival kit<\/a> a useful companion resource alongside these Calculus 1 topics.<\/p>\n\n<h2>Calculus 2 Topics<\/h2>\n\n<p>Calculus 2 extends the integral and differential equation work from Calculus 1 and introduces series, parametric equations, and polar coordinates. Students preparing for <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/ap-calculus-bc\/\">AP Calculus BC<\/a> will cover the majority of these topics. The full topic list for Calculus 2 is below.<\/p>\n\n<h3>Integrals Review<\/h3>\n<ul>\n<li>Accumulations of change<\/li>\n<li>Approximation with Riemann sums<\/li>\n<li>Summation notation<\/li>\n<li>Riemann sums in summation notation<\/li>\n<li>Defining integrals with Riemann sums<\/li>\n<li>Fundamental theorem of calculus and accumulation functions<\/li>\n<li>Interpreting the behavior of accumulation functions<\/li>\n<li>Properties of definite integrals<\/li>\n<li>Fundamental theorem of calculus and definite integrals<\/li>\n<li>Reverse power rule<\/li>\n<li>Indefinite integrals of common functions<\/li>\n<li>Definite integrals of common functions<\/li>\n<\/ul>\n\n<h3>Integration Techniques<\/h3>\n<ul>\n<li>Integrating with u-substitution<\/li>\n<li>Integrating using long division and completing the square<\/li>\n<li>Integrating using trigonometric identities<\/li>\n<li>Trigonometric substitution<\/li>\n<li>Integration by parts<\/li>\n<li>Integrating using linear partial fractions<\/li>\n<li>Improper integrals<\/li>\n<\/ul>\n\n<h3>Differential Equations (Calculus 2)<\/h3>\n<ul>\n<li>Verifying solutions for differential equations<\/li>\n<li>Sketching slope fields<\/li>\n<li>Reasoning using slope fields<\/li>\n<li>Approximation with Euler&#8217;s method<\/li>\n<li>Separation of variables<\/li>\n<li>Particular solutions to differential equations<\/li>\n<li>Exponential models<\/li>\n<li>Logistic models<\/li>\n<\/ul>\n\n<h3>Applications of Integrals (Calculus 2)<\/h3>\n\n<p>Students who find probability distributions challenging alongside integral applications may benefit from this <a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/choosing-the-right-probability-distribution-a-statistics-guide-for-engineers\/\">statistics guide for engineers on choosing the right probability distribution<\/a>.<\/p>\n\n<ul>\n<li>Average value of a function<\/li>\n<li>Straight-line motion<\/li>\n<li>Non-motion applications of integrals<\/li>\n<li>Area: vertical area between curves<\/li>\n<li>Area: horizontal area between curves<\/li>\n<li>Area: curves that intersect at more than two points<\/li>\n<li>Volume: squares and rectangles cross-sections<\/li>\n<li>Volume: triangles and semicircles cross-sections<\/li>\n<li>Volume: disc method (revolving around x- and y-axes)<\/li>\n<li>Volume: disc method (revolving around other axes)<\/li>\n<li>Volume: washer method (revolving around x- and y-axes)<\/li>\n<li>Volume: washer method (revolving around other axes)<\/li>\n<li>Arc length<\/li>\n<\/ul>\n\n<h3>Parametric Equations, Polar Coordinates, and Vector-Valued Functions<\/h3>\n<ul>\n<li>Parametric equations<\/li>\n<li>Second derivatives of parametric equations<\/li>\n<li>Arc length: parametric curves<\/li>\n<li>Vector-valued functions<\/li>\n<li>Planar motion<\/li>\n<li>Polar functions<\/li>\n<li>Area: polar regions (single curve)<\/li>\n<li>Area: polar regions (two curves)<\/li>\n<li>Arc length: polar curves<\/li>\n<\/ul>\n\n<h3>Series<\/h3>\n\n<p>Students working through series convergence tests often encounter hypothesis-testing logic in their statistics courses as well; this <a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/how-to-solve-hypothesis-testing-complete-step-by-step-stats-guide\/\">step-by-step guide to hypothesis testing<\/a> covers that parallel reasoning in detail. Those preparing specifically for <a href=\"https:\/\/www.myengineeringbuddy.com\/subject\/ap-calculus-ab\/\">AP Calculus AB<\/a> should note that series topics are generally not part of the AB curriculum.<\/p>\n\n<ul>\n<li>Convergent and divergent infinite series<\/li>\n<li>Infinite geometric series<\/li>\n<li>nth-term test<\/li>\n<li>Integral test<\/li>\n<li>Harmonic series and p-series<\/li>\n<li>Comparison tests<\/li>\n<li>Alternating series test<\/li>\n<li>Ratio test<\/li>\n<li>Absolute and conditional convergence<\/li>\n<li>Alternating series error bound<\/li>\n<li>Taylor and Maclaurin polynomials<\/li>\n<li>Error bound<\/li>\n<li>Power series<\/li>\n<li>Function as a geometric series<\/li>\n<li>Maclaurin series of e\u02e3, sin(x), and cos(x)<\/li>\n<li>Representing functions as power series<\/li>\n<\/ul>\n\n<p>Check the <a href=\"https:\/\/en.wikipedia.org\/wiki\/List_of_calculus_topics\" target=\"_blank\" rel=\"noopener\">Wikipedia page on calculus topics<\/a> to see the complete list of topics in Calculus 1, 2 and more.<\/p>\n\n<p>We at My Engineering Buddy offer live online tutoring sessions covering all of the above topics, including guidance on homework, lab reports, and projects as learning support. You can reach us on WhatsApp at +91 8971 383660 or by email at meb@myengineeringbuddy.com.<\/p>\n\n<h2>Related Reading<\/h2>\n<ul>\n<li><a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/struggling-ap-calculus-find-tutor-score-5\/\">Struggling with AP Calculus? How to Find a Tutor and Score a 5<\/a><\/li>\n<li><a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/choose-algebra-tutor-verification-checklist-2026\/\">How to Choose an Algebra Tutor: Verification Checklist 2026<\/a><\/li>\n<li><a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/photomath-cheating-guide\/\">Photomath and Cheating: What Students and Parents Should Know<\/a><\/li>\n<li><a href=\"https:\/\/www.myengineeringbuddy.com\/blog\/ap-calculus-tutors-engineering-success\/\">AP Calculus Tutors and Engineering Success<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Key Takeaways Calculus is divided into Calculus 1, Calculus 2,  [&#8230;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-11249","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/posts\/11249","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/comments?post=11249"}],"version-history":[{"count":1,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/posts\/11249\/revisions"}],"predecessor-version":[{"id":12125,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/posts\/11249\/revisions\/12125"}],"wp:attachment":[{"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/media?parent=11249"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/categories?post=11249"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.myengineeringbuddy.com\/blog\/wp-json\/wp\/v2\/tags?post=11249"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}