TENSOR CALCULUS for Engineers & Machine Learning

TENSOR CALCULUS FOR ENGINEERS & MACHINE LEARNING
A Step-by-Step Guide with Applications in AI, Physics, Robotics & Optimization

Struggling to connect the math in physics with the tensors used in deep learning?

This book bridges the gap.

Whether you're an engineering student, machine learning practitioner, or physics learner, Tensor Calculus for Engineers & Machine Learning gives you a clear, practical path to mastering one of the most powerful mathematical tools in modern science.

Instead of treating tensors as abstract theory or just arrays in code, this book shows you how they work across disciplines-using the same notation, the same logic, and real-world applications.

• Understand tensors from first principles-without confusion or intimidation
• Master index notation and Einstein summation with ease
• Perform tensor operations used in engineering and AI
• Derive gradients for neural networks, including attention mechanisms
• Apply tensor calculus to mechanics, robotics, and optimization
• Use NumPy, PyTorch, and einsum like a professional

• Combines engineering + AI applications in every chapter
• Focuses on intuition first, then formal understanding
• Includes 165+ practice problems with full solutions
• Features a complete transformer backpropagation walkthrough
• Designed for real-world problem solving, not memorization

• Engineering students (mechanical, electrical, civil, robotics)
• Machine learning and AI practitioners
• Physics students and applied mathematicians
• Anyone who wants to truly understand tensors-not just use them

• Basic linear algebra
• Single-variable calculus (multivariable helpful but reviewed inside)

Stop memorizing formulas. Start understanding the language behind modern AI and engineering.

Master tensor calculus-and unlock the mathematics behind today's most powerful technologies.