Engineering Mathematics-I syllabus
SPPU First Year Engineering, 2024 pattern. Course code BSC-101-BES. Five units, 40 hours of theory, with the marks scheme, outcomes and books taken from the official syllabus book.
Unit-wise syllabus
Unit I: Single Variable Calculus
- Rolle’s Theorem
- Mean Value Theorems
- Taylor's and Maclaurin's Series
- Indeterminate Forms
- L' Hospital's Rule
- Fourier series (Full range & Half range)
- Harmonic analysis
Unit II: Multivariable Calculus – Partial Differentiation
- Limits & Continuity of several variables
- Partial Derivatives
- Euler's Theorem on Homogeneous functions
- Partial derivative of Composite Function
- Total Derivative
- Change of Independent variables
Unit III: Applications of Partial Differentiation
- Jacobian and its applications
- Errors and Approximations
- Maxima and Minima of functions of two variables
- Lagrange's method of undetermined multipliers
Unit IV: Matrices and System of Linear Equations
- Rank of a Matrix
- System of Linear Equations
- Linear Dependence and Independence
- Linear and Orthogonal Transformations
- Applications in Engineering
Unit V: Eigen Values, Eigen Vectors and Diagonalization
- Eigen Values and Eigen Vectors
- Cayley Hamilton theorem
- Diagonalization of a matrix
- Reduction of Quadratic forms to Canonical form
- Applications in Engineering
Where the hours go
- Unit I: Single Variable Calculus8 h
- Unit II: Multivariable Calculus – Partial Differentiation8 h
- Unit III: Applications of Partial Differentiation8 h
- Unit IV: Matrices and System of Linear Equations8 h
- Unit V: Eigen Values, Eigen Vectors and Diagonalization8 h
Effort by unit
Share of teaching hours per unit. The syllabus does not publish marks per unit, so this shows where the course time goes, not how the paper is weighted.
Marks and credits
| Head | Marks | Credit |
|---|---|---|
| Theory: CCE | 30 | 3 |
| Theory: End-Semester | 70 | |
| Tutorial / term work | 25 | 1 |
The prerequisites listed in the syllabus are differentiation, integration, maxima and minima, matrices and determinants. The course aims to build the calculus, Fourier series and linear algebra needed in later engineering subjects.
Course outcomes
- CO1Apply mean value theorems and their generalizations leading to Taylor and Maclaurin series. Determine the Fourier series representation and harmonic analysis of periodic functions.
Covers Unit I - CO2Evaluate derivative functions of several variables.
Covers Unit II - CO3Apply the Jacobian to find partial derivatives of implicit functions and functional dependence. Use partial derivatives for errors, approximations and extreme values.
Covers Unit III - CO4Use matrices and linear algebra to analyse systems of linear equations, linear dependence and independence, and linear and orthogonal transformations.
Covers Unit IV - CO5Determine eigen values and eigen vectors, diagonalize a matrix and reduce a quadratic form to canonical form.
Covers Unit V
A study order that follows the syllabus
- 1Unit I: Single Variable Calculus8 hours
- 2Unit II: Multivariable Calculus – Partial Differentiation8 hours
- 3Unit III: Applications of Partial Differentiation8 hours
- 4Unit IV: Matrices and System of Linear Equations8 hours
- 5Unit V: Eigen Values, Eigen Vectors and Diagonalization8 hours
This is a suggestion, not part of the syllabus. Unit II (partial derivatives, Euler's theorem, total derivative) is what Unit III (Jacobian, errors, maxima and minima) builds on, so do them in that order. In the same way, Unit IV (rank, linear systems, transformations) comes before Unit V (eigen values, Cayley-Hamilton, diagonalization). Unit I stands alone, so it is a good starting point or a break between the two blocks.
Books
Text books
- Higher Engineering Mathematics by B. V. Ramana (Tata McGraw Hill)
- Higher Engineering Mathematics by B. S. Grewal (Khanna Publication)
Reference books
- Advanced Engineering Mathematics by Erwin Kreyszig (Wiley Eastern Ltd.)
- Advanced Engineering Mathematics by M. D. Greenberg (Pearson Education)
- Advanced Engineering Mathematics by Peter V. O’Neil (Thomson Learning)
- Thomas’ Calculus by George B. Thomas (Addison-Wesley, Pearson)
- Applied Mathematics (Vol. I & II) by P. N. Wartikar and J. N. Wartikar (Vidyarthi Griha Prakashan, Pune)
- Elementary Linear Algebra by Ron Larson and David C. Falvo (Houghton Mifflin Harcourt)
Video lectures
The syllabus lists one NPTEL / YouTube playlist for this course: Engineering Mathematics-I playlist.
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Open Engineering Mathematics-I in the appFAQ
How many credits is Engineering Mathematics-I in the SPPU 2024 pattern?
BSC-101-BES carries 4 credits: 3 for theory (3 hours a week) and 1 for the tutorial (1 hour a week).
How are the marks split?
Theory is graded out of 100: CCE (continuous internal evaluation) 30 and End-Semester 70. Term work is a separate 25 marks tied to the tutorial credit.
How many units are there?
Five units of 8 hours each, 40 hours in total: single variable calculus and Fourier series, partial differentiation, its applications, matrices and linear systems, and eigen values with diagonalization.
What do I need to pass the theory head?
The college copy of the SPPU rules asks for at least 12 in CCE, at least 28 in the End-Semester exam and at least 40 in total. Check your own college notice for the exact rule that applies to you.
Which books does the syllabus list?
Text books: B. V. Ramana and B. S. Grewal, both titled Higher Engineering Mathematics. Six reference books are listed too, including Kreyszig and Thomas’ Calculus.
Is there an official video course?
The syllabus lists one NPTEL / YouTube playlist for this course. It is linked on this page.