Integral Calculus for Physicists

Name: Integral Calculus for Physicists
Rating: 5.0 (7 reviews)

Indefinite and Definite Integrals

Created byKalyan Dutt Shatdarsanam

Last updated 10/2021

English

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What you'll learn

Understand integration as reverse operation of differentiation
Understanding integration by substitution and integration by parts
understand definite integrals and their techniques
understand the geometrical meaning of integration and how integration and differentiation are reverse operations (Fundamental theorem of calculus))

Course content

3 sections • 22 lectures • 3h 57m total length

Introduction4:02
Explore the second half of calculus by introducing integration as adding infinitely many infinitesimal terms, and see how it serves as the reverse operator of differentiation.
Symbol for Integration and writing Integrals from Differentiation5:35
Explore the integration symbol and notation, specify the function and the integration variable, and demonstrate reversing differentiation with examples such as x^2 and log x.
Indefinite Integrals and Why Constant is needed12:52
Explore indefinite integrals and the role of constants, converting differentiation rules into integrals, and applying standard power, exponential, and trigonometric formulas with plus c.
Properties of Integrals3:27
Explore the two basic properties of integrals—constants factor outside and linearity for sums—along with the constant of integration, and preview techniques like integration by parts and substitution.
Integration by Substitution11:52
Explore integration by substitution as a change of variable technique, transforming integrals and using differentiation with respect to x; recognize when substitution yields a closed form or an infinite series.
Integrals with variable of integration replaced with linear term5:00
Learn a substitution-based theorem for integrals with a linear change of variable, ax+b; adjust by the coefficient and offset. Prove by substitution and see examples, noting it fails for quadratics.
Integration by Substitution Example 14:45
Explore integration by substitution with physics applications, solving a challenging integral and showing how substitution simplifies expressions in electrostatics and electromagnetism, including handling limits.
Integration by Substitution Examples 2 and 35:04
practice integration by substitution using algebraic and trig substitutions, transforming integrals via u-substitution (x = u) and t-substitution, and deriving results in terms of arcsin and arccos.
An example on Integration using Partial Fraction3:04
Learn partial fractions to simplify rational integrals by transforming the denominator into two terms, and preview integration by substitution and by parts.
Integration by Parts11:54
Use integration by parts with the IlOt rule to choose the first function, turning a product into u v minus ∫ v du, with x sin x and log x.

Integration Practice Session 113:16
Practice integration using power rules, the natural log for x^-1, and substitution techniques. Solve multiple questions to reinforce antiderivatives and verification.
Integration Practice Session 211:16
Integral calculus for physicists offers an integration practice session 2, applying integration by parts, substitution, and trigonometric transformations to solve and simplify a variety of integrals.
Integration Practice Session 321:09
Learn and apply integration by substitution to solve diverse integrals, verify results by differentiation, and practice with substitution techniques and trigonometric substitutions.
Integration Practice Session 421:13
Master integration by parts through diverse examples, selecting the first function from polynomials, logarithmic, trigonometric, or exponential forms, and verify results by differentiation.

Definite Integrals Introduction10:29
Explore how definite integrals, unlike indefinite ones, eliminate the arbitrary constant by evaluating at the upper and lower limits and subtracting, with examples like ∫0^1 x^2 dx.
Properties of Definite Integrals13:44
This lecture explains key properties of definite integrals, including zero for equal limits, sign change with reversed limits, substitution x by a+b−x, and even/odd symmetry examples.
Problems on Definite integrals13:21
Master techniques for definite integrals using symmetry and substitution, showing how replacing x with -x and adding paired integrals yields results such as 5/4.
Geometrical Meaning of a Definite Integral7:23
Explore the geometrical meaning of the definite integral as the area between a curve and the x-axis, bounded by x = a and x = b.
Integrals as Riemman Sum11:35
Explore calculating the area under the curve y = x^2 from 0 to 1 using Riemann sums, refining partitions to approach the exact area and introducing integration.
An Example on Riemman Sums (Lower and Upper Areas)20:43
Explore calculating the area under y = x^2 from 0 to 1 using left and right Riemann sums, and see how the integral emerges as a limit.
General discussion on Area under Curve as Riemman Sum11:59
Explore how to approximate area under a continuous curve by partitioning [a,b] into rectangles and forming a Riemann sum with right-end heights, leading to the definite integral as n→∞.
Fundamental Theorem of Calculus (How Integration is reverse of Differentiation )14:05
Explore the fundamental theorem of calculus, showing how integration computes the area under a curve with limits and how differentiation acts as the inverse of integration.

Requirements

Differential Calculus is a must. A good knowledge of trigonometry and basics of coordinate geometry

Description

I have made this course in such a way that you can easily understand integration and how to solve integrals., We begin by looking at integration as reverse operation of differentiation. You will be introduced the symbol of integration and how can you write using this symbol all formulae of integration from differentiation. The role of integration constant is told in the simplest possible way. This is followed by some basic properties of integrals and then you are introduced to techniques of integration. I have focused on two main techniques mainly integration by substitution and integration by parts. I have done lots of problems to instill confidence in you. Finally I have introduced Definite Integrals, the role of limits (upper and lower), finding area using integration, integration as Riemman sum and at last the fundamental theorem of calculus. Every discussion is followed by relevant illustrations. I have also dealt in these lectures , properties of definite integrals with the help of which some problems can be solved in much easier ways, Sufficient number of such questions are discussed in the lectures. Finally the proof that i gave as fundamental theorem is a very simple one stripped of all complicated mathematical rigors.

Who this course is for:

Any adult interested in physics and wanting to learn it feom calculus perspective
All students above 18 years
Parents whose children are below 18 years but preparing for competitive exams like JEE and NEET

Integral Calculus for Physicists

What you'll learn

Explore related topics

Course content

Introduction10 lectures • 1hr 8min

Practise Session Lectures4 lectures • 1hr 7min

Definite Integrals8 lectures • 1hr 43min

Requirements

Description

Who this course is for: