MAE101 - Mathematics for Engineering

Course description

• MAE101 Mathematics for Engineering

  • Instructor: Dr. Trịnh Hoàng Minh

    • Email: trinhhoangminhbk@gmail.com; minhtrinh@ieee.org

  • Time allocation: 20 slots (07/09 – 10/11/2023)

  • Assessment and grading:

    • Homework assignment: 30%

    • Progress test: 30% (Test 1: 40 min., 20 questions; Test 2 & 3: 30 min. (15 questions))

    • Final exam: 40% (60 min., 50 questions)

  • Textbooks:

    • E. Herman & G. Strang, Calculus 1 & 2, Openstax  https://openstax.org/details/books/calculus-volume-1,  https://openstax.org/details/books/calculus-volume-2

    • W. K. Nicholson, Linear algebra with Applications, LyryX Ver 2021-A https://lyryx.com/linear-algebra-applications/

  • Reading:

    • https://assets.openstax.org/oscms-prodcms/media/documents/OpenStax.Effective.Reading.and.Notetaking.Guide_E7WFZSP.pdf

    • https://www.ocw.mit.edu/courses/18-01-calculus-i-single-variable-calculus-fall-2020/

    • https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/

    • Slides MAE101, FPT University

    • Nguyễn Đình Trí, Tạ Văn Đĩnh, Nguyễn Hồ Quỳnh. Bài tập Toán cao cấp Tập 1 và Tập 2, NXB Giáo dục

Main contents

• Calculus:

  • Functions and Graphs

  • Limits

  • Derivatives and its applications

  • Integration and its applications

  • Techniques of Integration

• Linear Algebra:

  • Systems of linear equations

  • Matrix algebra

  • Determinant and diagonalization

  • Vector geometry

  • The vevector space Rn

Course's outlines

Survey and Course introduction.

1 Functions and graphs

1.1 Review of functions

1.2. Basic classes of functions

1.3 Inverse functions

2 Limits

2.1 The limit of a function

2.2 The limit laws

2.3 Continuity

3 Derivatives

3.1 Derivatives and its meaning

3.2 Differentiation rules

3.3 Derivatives of inverse functions

4 Applications of derivatives

4.1 Maxima and minima

4.2 The mean value theorem

4.3 The shape of graphs

4.4 Applied optimization problem

4.5 Linear approximations and differentials

4.6 Newton’s method

5 Integration

5.1 Antiderivative and indefinite integral

5.2 Area approximation

5.3 Definite integral

5.4 Fundamental theorem of calculus

5.5 The net change theorem

6 Techniques of integration

6.1 Improper integrals

6.2 Comparison theorem

Review Chapters 1-6

Review exercises

Graded Assignment 1

Progress test 1

7 Systems of linear equations

7.1 Solutions and elementary operations

7.2 Gaussian elimination

7.3 Homogeneous equations

7.4 Applications

8 Matrix algebra

8.1 Matrix addition, scalar multiplication, and transposition

8.2 Matrix-vector multiplication

8.3 Matrices and transformations

8.4 Matrix multiplication

8.5 Matrix inverses

8.6 Elementary matrices

8.7 Application in an input-output economic model

9 Determinant and diagonalization

9.1 The cofactor expansion

9.2 Determinant and matrix inverses

9.3 Diagonalization and eigenvalues

Review Chapters 7-9

Review exercises

Progress exam 2

Graded Assignment 2

10 Vector geometry

10.1 Vectors and lines

10.2 Projections and planes

10.3 Cross product

10.4 Linear operators on R3

10.4 An application on computer graphics

11 The vector space Rn

11.1 Subspaces and spanning

11.2 Independence and dimension

11.3 Orthogonality

11.4 Rank of a matrix

11.5 Application in least square approximation

Review Chapters 10, 11

Review exercises.

Progress test 3

Graded Assignment 3

All slides can be downloaded here