Course11110512160 lectures
Engineering Mathematics - I
Prof. Jitendra Kumar · IIT Kharagpur
About
This course is about the basic mathematics that is fundamental and essential component in all streams of undergraduate studies in sciences and engineering. The course consists of topics in differential calculus,integral calculus, linear algebra and differential equations with applications to various engineering problems. This course will cover the following main topics: Mean Value Theorems; Indeterminate Forms; Taylor's and Maclaurin's Theorems. Partial Derivatives; Differentiability; Taylor's Expansion of Functions of Several Variables. Maxima and Minima. Improper Integrals. Differentiation under Integral Sign (Leibnitz rule).Multiple Integrals and their Properties. Applications of Multiple Integrals. System of Linear Equations. Vector Spaces; Basis and Dimension of a Vector Space. Rank of a Matrix and its Properties. Linear Transformation. Eigenvalues and Eigen vectors. Diagonalization . First Order Differential Equations. Higher Order Differential Equations with Constant Coefficients. Cauchy-Euler Equations.
Intended audience: All branches of science and engineering
Lectures
Week 1 :
- Lecture 01 : Rolle’s Theorem
- Lecture 02 : Mean Value Theorems
- Lecture 03 : Indeterminate Forms (Part ‐1)
- Lecture 04 : Indeterminate Forms (Part ‐2)
- Lecture 05 : Taylor Polynomial and Taylor Series
Week 2 :
- Lecture 06 : Limit of Functions of Two Variables
- Lecture 07 : Evaluation of Limit of Functions of Two Variables
- Lecture 08 : Continuity of Functions of Two Variables
- Lecture 09 : Partial Derivatives of Functions of Two Variables
- Lecture 10 : Partial Derivatives of Higher Order
Week 3 :
- Lecture 11 : Derivative & Differentiability
- Lecture 12 : Differentiability of Functions of Two Variables
- Lecture 13 : Differentiability of Functions of Two Variables (Cont.)
- Lecture 14 : Differentiability of Functions of Two Variables (Cont.)
- Lecture 15 : Composite and Homogeneous Functions
Week 4 :
- Lecture 16 : Taylor’s Theorem for Functions of Two Variables
- Lecture 17 : Maxima & Minima of Functions of Two Variables
- Lecture 18 : Maxima & Minima of Functions of Two Variables (Cont.)
- Lecture 19 : Maxima & Minima of Functions of Two Variables (Cont.)
- Lecture 20 : Constrained Maxima & Minima
Week 5 :
- Lecture 21 : Improper Integrals
- Lecture 22 : Improper Integrals (Cont.)
- Lecture 23 : Improper Integrals (Cont.)
- Lecture 24 : Improper Integrals (Cont.)
- Lecture 25 : Beta & Gamma Function
Week 6 :
- Lecture 26 : Beta & Gamma Function (Cont.)
- Lecture 27 : Differentiation Under Integral Sign
- Lecture 28 : Double Integrals
- Lecture 29 : Double Integrals (Cont.)
- Lecture 30 : Double Integrals (Cont.)
Week 7 :
- Lecture 31 : Integral Calculus –Double Integrals in Polar Form
- Lecture 32 : Integral Calculus –Double Integrals: Change of Variables
- Lecture 33 : Integral Calculus – Double Integrals: Surface Area
- Lecture 34 : Integral Calculus –Triple Integrals
- Lecture 35 : Integral Calculus – Triple Integrals (Cont.)
Week 8 :
- Lecture 36 : System of Linear Equations
- Lecture 37 : System of Linear Equations – Gauss Elimination
- Lecture 38 : System of Linear Equations – Gauss Elimination (Cont.)
- Lecture 39 : Linear Algebra - Vector Spaces
- Lecture 40 : Linear Independence of Vectors
Week 9 :
- Lecture 41 : Vector Spaces –Spanning Set
- Lecture 42 : Vector Spaces –Basis and Dimension
- Lecture 43 : Rank of a Matrix
- Lecture 44 : Linear Transformations
- Lecture 45 : Linear Transformations (cont.)
Week 10 :
- Lecture 46 : Eigenvalues & Eigenvectors
- Lecture 47 : Eigenvalues & Eigenvectors (Cont.)
- Lecture 48 : Eigenvalues & Eigenvectors (Cont.)
- Lecture 49 : Eigenvalues & Eigenvectors (Cont.)
- Lecture 50 : Eigenvalues & Eigenvectors: Diagonalization
Week 11 :
- Lecture 51 : Differential Equations - Introduction
- Lecture 52 : First Order Differential Equations
- Lecture 53 : Exact Differential Equations
- Lecture 54 : Exact Differential Equations (Cont.)
- Lecture 55 : First Order Linear Differential Equations
Week 12 :
- Lecture 56 : Higher Order Linear Differential Equations
- Lecture 57 : Solution of Higher Order Homogeneous Linear Equations
- Lecture 58 : Solution of Higher Order Non-Homogeneous Linear Equations
- Lecture 59 : Solution of Higher Order Non-Homogeneous Linear Equations (cont.)
- Lecture 60 : Cauchy-Euler Equations
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Kharagpur
- Department
- Mathematics
- Teacher
- Prof. Jitendra Kumar
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed