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Ace your Linear Algebra exams with this complete set of notes on Vector Subspaces! Ideal for engineering, mathematics, and applied science students, these notes cover everything you need to understand and master the topic: Definition and Properties of Vector Subspaces – Clear explanations Span, Linear Independence, and Basis – Step-by-step methods Dimension Theorem – Solved examples for easy understanding Subspace Operations – Intersection, sum, and related exercises Worke...

Ace your exams and master complex analysis with this comprehensive set of notes on Complex Integration! Perfect for engineering, mathematics, and applied science students, these notes cover everything you need: Contour Integration – Step-by-step methods with examples Cauchy Integral Theorem & Formula – Clear explanations and solved problems Cauchy Residue Theorem – How to evaluate integrals using residues Singularities – Classification and application Evaluation of Real In...

Standard Test Signals and Time Domain Analysis in Control Systems explain how a system responds to inputs like impulse, step, ramp, and parabolic signals. These concepts help evaluate transient and steady-state behavior using parameters such as rise time, settling time, peak time, overshoot, damping ratio, and natural frequency.

These notes cover State Space Analysis in a clear, simple and exam-focused way. Perfect for B.Tech (ECE/EEE/CSE), GATE, diploma students, and university exams. Includes complete coverage of: • State variables and state model • State equation + output equation • How to convert transfer function to state space • Phase variable, diagonal, and Jordan canonical forms • State Transition Matrix (STM) and its properties •

These Control Systems notes cover all major topics in a simple, clear, exam-focused way. Perfect for B.Tech (ECE/EEE/CSE), Diploma, GATE, university exams, and quick revision. Includes: Time domain analysis (transient & steady-state) • Stability analysis – Routh-Hurwitz • Root locus method (construction + numericals) • Frequency response – Bode, Nyquist, Polar plots • Gain margin, phase margin Clean and neat handwritten notes Step-by-step solved problems Formula she...

These Control Systems notes cover all major topics in a simple, clear, exam-focused way. Perfect for B.Tech (ECE/EEE/CSE), Diploma, GATE, university exams, and quick revision. Includes: • System basics – open/closed loop, transfer functions • Block diagram reduction • Signal flow graph + Mason’s gain formula Clean and neat handwritten notes Step-by-step solved problems Formula sheet included Perfect for last-minute study + scoring full marks No textbook theory – on...

Phyton code in english

Summary - Phyton (Phyton code)

Notes for cat