Calculus

• • • • • Classes • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • n th Order Linear Equations • • • • • • • • • • • • • • • • • • • • • • • • • Extras • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Misc Links • • • • • • You appear to be on a device with a "narrow" screen width ( i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Calculus III Here are my online notes for my Calculus III course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus III or nee...

Multiple Integrals • Integral Applications • Limit of Sum • Area under curve • Area between curves • Area under polar curve • Volume of solid of revolution • Arc Length • Function Average • Integral Approximation • Riemann Sum New • Trapezoidal New • Simpson's Rule New • Midpoint Rule New • Series • Convergence • Geometric Series Test • Telescoping Series Test • Alternating Series Test • P Series Test • Divergence Test • Ratio Test • Root Test • Comparison Test • Limit Comparison Test • Integral Test • Absolute Convergence • Power Series • Radius of Convergence • Interval of Convergence • ODE • Linear First Order • Linear w/constant coefficients • Separable • Bernoulli • Exact • Second Order • Homogenous • Non Homogenous • Substitution • System of ODEs • IVP using Laplace • Series Solutions • Method of Frobenius • Multivariable Calculus • Partial Derivative New • Implicit Derivative New • Tangent to Conic New • Multi Variable Limit New • Multiple Integrals New • Gradient New • Divergence New • Extreme Points New • Laplace Transform • Transform • Inverse • Taylor/Maclaurin Series • Taylor Series • Maclaurin Series • \square^ (2\times2) (2\times3) (3\times3) (3\times2) (4\times2) (4\times3) (4\times4) (3\times4) (2\times4) (5\times5) (1\times2) (1\times3) (1\times4) (1\times5) (1\times6) (2\times1) (3\times1) (4\times1) (5\times1) (6\times1) (7\times1) \mathrm + • \lim_,\:(-1,\:1) • Show More

Recently, there were a few articles dealing with this topic. Here are a few thoughts which I plan to expand more in the future. • Calculus is essential for many other fields and sciences. • It is a prototype of a though construction and part of culture. • Teaching calculus has long tradition. Its teaching can be learned. • If we wanted to teach something else, what would replace it? • Calculus develops thinking and problem solving skills. • Example of an article asking this question: • Added August 30, 2017: Why calculus is valuable Calculus is lucrative business. Calculus is made to gold in many industries. Today! Geography (google earth), computer vision (autonomous driving of cars), Photography (panoramas), artificial intelligence (optical character recognition), robots (mars bots), computer games (world of warcraft), Movies (avatar), network visualization (social networks). We live in a time where calculus is made to gold. If linear algebra is added to calculus (page rank example), then applications get even bigger. There is a gold rush on calculus. It currently is responsible for billions of profit. Why calculus is a prototype Calculus helped to understand of what we are and to plan where we go. No other field of mathematics is so rich in history and culture than calculus. From fundamental geometry like Pythagoras as part of vector calculus, measuring volumes with ideas of Archimedes, to deal with velocities and forces which was essential in the development of astrono...

: Parametric equations, polar coordinates, and vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions

Search • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Calculus Calculus — 2 Subjects, 12 Units Each Mathematics is the common language of science and engineering, and calculus is a part of mathematics that is essential for understanding and describing many aspects of the physical world. The two-subject calculus General Institute Requirement (GIR) is designed to introduce the fundamental concepts of the calculus and provide the mathematical foundations on which subjects across MIT build. The Mathematics GIR consists of 18.01 and 18.02 or equivalent courses. The 18.01 requirement can also be fulfilled through suitable scores on tests such as Advanced Placement exams or by passing Advanced Standing Exams or by transfer credit. 18.02 can be fulfilled by passing an Advanced Standing E...

Textbook Published in 1991 by The complete textbook is also available as a single file. ( Highlights of Calculus MIT Professor Gilbert Strang has created › Textbook Components • Table of Contents ( • Answers to Odd-Numbered Problems ( • Equations ( ChapterS FILES 1: Introduction to Calculus, pp. 1-43 1.1 Velocity and Distance, pp. 1-7 1.2 Calculus Without Limits, pp. 8-15 1.3 The Velocity at an Instant, pp. 16-21 1.4 Circular Motion, pp. 22-28 1.5 A Review of Trigonometry, pp. 29-33 1.6 A Thousand Points of Light, pp. 34-35 1.7 Computing in Calculus, pp. 36-43 Chapter 1 - complete ( Chapter 1 - sections: 1.1 - 1.4 ( 1.5 - 1.7 ( 2: Derivatives, pp. 44-90 2.1 The Derivative of a Function, pp. 44-49 2.2 Powers and Polynomials, pp. 50-57 2.3 The Slope and the Tangent Line, pp. 58-63 2.4 Derivative of the Sine and Cosine, pp. 64-70 2.5 The Product and Quotient and Power Rules, pp. 71-77 2.6 Limits, pp. 78-84 2.7 Continuous Functions, pp. 85-90 Chapter 2 - complete ( Chapter 2 - sections: 2.1 - 2.4 ( 2.5 - 2.7 ( 3: Applications of the Derivative, pp. 91-153 3.1 Linear Approximation, pp. 91-95 3.2 Maximum and Minimum Problems, pp. 96-104 3.3 Second Derivatives: Minimum vs. Maximum, pp. 105-111 3.4 Graphs, pp. 112-120 3.5 Ellipses, Parabolas, and Hyperbolas, pp. 121-129 3.6 Iterations x[n+1] = F(x[n]), pp. 130-136 3.7 Newton’s Method and Chaos, pp. 137-145 3.8 The Mean Value Theorem and l’Hôpital’s Rule, pp. 146-153 Chapter 3 - complete ( Chapter 3 - sections: 3.1 - 3.4 ( 3.5 - 3....

Calculus. It’s a word that strikes fear in many students. But one of the main struggles students have isn’t with calculus itself. It’s with the foundational algebra and trigonometry concepts that are applied in calculus. This is why we stress the importance of reviewing past math classes and truly understanding the material while you’re in the class. That way, when you do get to subjects such as calculus, you have a foundation to build on! So today we’re going to simplify calculus a bit. This includes key concepts from algebra and trig that you’ll need to know as well as tips specific to calculus. • Know the definitions As with any math class, and you’ve heard us say this many times already, but you’re going to hear it again: KNOW THE DEFINITIONS. This is especially important in calculus. In this subject, you learn about things called limits , derivatives , and integrals , each of which has a very conceptual definition. This means that one problem can be phrased in 10 different ways. If you don’t know these definitions, you won’t have any idea what you’re being asked. • Learn to walk You learn calculus concepts in a very specific order: limits, derivatives, integrals, series, higher dimensions, etc. Cool thing is that there’s actually a reason for this. It’s like learning to walk by taking one step at a time before you start to run and jump. Just remember to focus on one thing at a time, all the while keeping in mind that everything you learn is based on the previous topic...

: Parametric equations, polar coordinates, and vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions : Parametric equations, polar coordinates, and vector-valued functions

Multiple Integrals • Integral Applications • Limit of Sum • Area under curve • Area between curves • Area under polar curve • Volume of solid of revolution • Arc Length • Function Average • Integral Approximation • Riemann Sum New • Trapezoidal New • Simpson's Rule New • Midpoint Rule New • Series • Convergence • Geometric Series Test • Telescoping Series Test • Alternating Series Test • P Series Test • Divergence Test • Ratio Test • Root Test • Comparison Test • Limit Comparison Test • Integral Test • Absolute Convergence • Power Series • Radius of Convergence • Interval of Convergence • ODE • Linear First Order • Linear w/constant coefficients • Separable • Bernoulli • Exact • Second Order • Homogenous • Non Homogenous • Substitution • System of ODEs • IVP using Laplace • Series Solutions • Method of Frobenius • Multivariable Calculus • Partial Derivative New • Implicit Derivative New • Tangent to Conic New • Multi Variable Limit New • Multiple Integrals New • Gradient New • Divergence New • Extreme Points New • Laplace Transform • Transform • Inverse • Taylor/Maclaurin Series • Taylor Series • Maclaurin Series • \square^ (2\times2) (2\times3) (3\times3) (3\times2) (4\times2) (4\times3) (4\times4) (3\times4) (2\times4) (5\times5) (1\times2) (1\times3) (1\times4) (1\times5) (1\times6) (2\times1) (3\times1) (4\times1) (5\times1) (6\times1) (7\times1) \mathrm + • \lim_,\:(-1,\:1) • Show More

• • • • • Classes • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • n th Order Linear Equations • • • • • • • • • • • • • • • • • • • • • • • • • Extras • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Misc Links • • • • • • You appear to be on a device with a "narrow" screen width ( i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Calculus III Here are my online notes for my Calculus III course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn Calculus III or nee...