LPU - Lovely Professional University
What you'll learn

This course enhances analytical, computational, and problem-solving skills through practical applications. Students will develop logical thinking, technical competency, and the ability to solve real-world engineering problems.

  • Introduction to matrices and elementary operations
  • Rank of matrix and applications
  • System of linear equations
  • Eigen values and Eigen vectors
  • Cayley-Hamilton theorem
  • General rules of differentiation and Derivatives of standard functions
  • Implicit and logarithmic differentiation
  • properties of indefinite integral
  • Integration by parts
  • Partial fractions and definite integrals
  • Rolle’s theorem
  • Mean value theorems
  • Taylor’s theorem
  • Maclaurin theorem and L'Hospital rule
  • CA-1
  • Functions of two variables and Limits and continuity
  • Partial derivatives
  • Total derivative and chain rule
  • Euler theorem for homogeneous functions
  • Maxima and Minima
  • Introduction to double integrals
  • Change of order of integration
  • Triple integrals
  • Change of variables
  • Area and volume using double integrals
  • Introduction to Fourier series and Euler formula
  • "Conditions for a Fourier Expansion and Functions having points of discontinuity
  • Change of Interval
  • Even/Odd functions and Half range series
  • Test 2

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Dr. Pardeep Kumar
Associate Professor

Dr. Pardeep Kumar is an Associate Professor in the School of Physical Sciences and Chemical Engineering at Lovely Professional University, Punjab, with over 15 years of teaching and research experience. He holds a Ph.D. in Mathematics, specializing in reliability engineering and multi-state system performance analysis under random operating conditions. He qualified the CSIR-NET with All India Rank 15 and GATE with AIR 98, reflecting his strong academic foundation. His research interests include reliability engineering, stochastic modelling, robotic and automated system reliability, and simulation techniques. He has published numerous research papers and book chapters in reputed international journals and edited volumes, contributing significantly to the field of mathematical modelling and system reliability. He is currently supervising a Ph.D. scholar and has guided postgraduate and undergraduate dissertations. Dr. Kumar is actively involved in curriculum development, research committees, and academic administration at the university. He is proficient in tools such as MATLAB and MAPLE and has strong expertise in data analysis and modelling. In addition to his academic achievements, he has been awarded Elite Topper (Top 1%) in multiple NPTEL certification courses, highlighting his commitment to continuous learning and excellence in his field.