Engineering Science Course

Lesson 1 • Functions and Graphical Analysis

Defines functions, domains, and transformations essential for modeling physical systems. Connects algebraic expressions to geometric interpretation.

Lesson 2 • Trigonometry for Engineering

Develops trigonometric identities and circular functions used in wave and force analysis. Provides tools for resolving vectors and periodic phenomena.

Lesson 3 • Coordinate Geometry and Vectors

Introduces Cartesian and polar coordinates alongside vector algebra for spatial reasoning. Prepares students for mechanics and field analysis.

Lesson 1 • Integration and the Fundamental Theorem

Introduces definite and indefinite integrals and the fundamental theorem of calculus. Builds skills for computing areas, volumes, and accumulated quantities.

Lesson 2 • Limits and Continuity

Defines limits rigorously and examines continuity conditions for engineering functions. Establishes the conceptual basis for differentiation and integration.

Lesson 3 • Applications of Derivatives

Applies derivatives to optimization, curve sketching, and related-rate problems in engineering. Links analytical results to physical interpretations.

Lesson 4 • Multivariable Calculus Essentials

Extends calculus to functions of several variables, covering partial derivatives and multiple integrals. Supports analysis of fields and surfaces in engineering.

Lesson 1 • Determinants and Their Applications

Covers determinant computation and its role in invertibility and geometric scaling. Connects determinants to system solvability and volume transformations.

Lesson 2 • Vector Spaces and Subspaces

Introduces abstract vector spaces, bases, and dimension for engineering function spaces. Supports understanding of solution sets and transformation kernels.

Lesson 3 • Matrices and Linear Systems

Defines matrix operations and methods for solving systems of linear equations. Provides the computational foundation for structural and circuit analysis.

Lesson 1 • Dynamics and Kinematics

Extends statics to moving systems, covering kinematics of particles and rigid bodies. Introduces work-energy and impulse-momentum methods for dynamic analysis.

Lesson 2 • Centroids and Moments of Inertia

Computes centroids and area moments of inertia for standard and composite cross-sections. Provides data needed for beam bending and column buckling analysis.

Lesson 3 • Truss and Frame Analysis

Analyzes internal forces in trusses and frames using method of joints and sections. Builds structural analysis skills for bridge and roof design.

Lesson 4 • Equilibrium of Rigid Bodies

Applies equilibrium conditions to determine unknown reactions in statically determinate systems. Connects force and moment balance to structural support design.

Lesson 1 • Heat Transfer Mechanisms

Covers conduction, convection, and radiation as the three modes of heat transfer. Applies Fourier's law and Newton's law of cooling to engineering design.

Lesson 2 • Thermodynamic Systems and Properties

Defines thermodynamic systems, state variables, and equations of state for ideal and real gases. Provides vocabulary and framework for all thermodynamic analysis.

Lesson 3 • First Law of Thermodynamics

Applies energy conservation to closed and open systems undergoing work and heat interactions. Connects internal energy changes to engineering process design.

Lesson 4 • Thermodynamic Cycles

Analyzes Rankine, Brayton, and refrigeration cycles for power and cooling applications. Develops skills for cycle optimization and component sizing.

Lesson 1 • Bernoulli and Energy Equations

Derives and applies Bernoulli's equation and the general energy equation to pipe and channel flows. Links pressure, velocity, and elevation in practical flow analysis.

Lesson 2 • Viscous Flow and Pipe Systems

Analyzes laminar and turbulent pipe flow, friction losses, and minor losses in piping networks. Applies Moody chart and Darcy-Weisbach equation to system design.

Lesson 3 • Fluid Kinematics

Describes fluid motion using streamlines, velocity fields, and the continuity equation. Connects flow visualization to conservation of mass in engineering systems.

Lesson 4 • Fluid Properties and Statics

Defines fluid properties and applies hydrostatic principles to pressure distribution and buoyancy. Establishes the physical basis for fluid system design.

Lesson 1 • Capacitors, Inductors, and Transients

Analyzes energy storage elements and first- and second-order transient circuit responses. Connects time-domain behavior to engineering control and signal applications.

Lesson 2 • Electromagnetic Field Principles

Introduces electric and magnetic fields, Gauss's law, Faraday's law, and Maxwell's equations. Connects field theory to transformer, motor, and antenna operation.

Lesson 3 • AC Circuit Analysis

Applies phasor methods and impedance to analyze sinusoidal steady-state AC circuits. Covers power factor and resonance for electrical system design.

Lesson 4 • Circuit Analysis Techniques

Introduces node-voltage, mesh-current, and superposition methods for complex circuit analysis. Enables systematic solution of multi-source and multi-loop networks.

Lesson 1 • Time-Domain System Response

Analyzes first- and second-order system responses to step, ramp, and impulse inputs. Connects time-domain specifications to physical performance requirements.

Lesson 2 • Stability Analysis

Applies Routh-Hurwitz criterion and root locus to assess and ensure closed-loop stability. Provides tools for identifying and correcting unstable system designs.

Lesson 3 • Laplace Transform Methods

Applies the Laplace transform to convert differential equations into algebraic transfer functions. Enables frequency-domain analysis of system dynamics and stability.

Lesson 4 • Feedback Controller Design

Designs proportional, integral, and derivative controllers to meet performance specifications. Applies compensation techniques to improve speed, accuracy, and stability.