Technological University (Hmawbi)

Blueprint B1 - Intermediate Student Book

Chapter 1
Functions: Even Functions, Odd Functions, Trigonometric Functions, Exponential Functions, Inverse Functions, and Logarithms.

Chapter 2

Limits and Continuity: Rates of Change, Limit Laws, Definitions of a limit, One-Sided Limits, Continuity Functions, Limit involving infinity.

Chapter 3

Differentiation: Derivatives, Differentiation Rules, Derivatives of Trigonometric Functions, Change Rule, Implicit Differentiation.

Chapter 4

Application of Derivatives: Extreme Values, Mean Value Theorem, Monotonic Functions, Concavity and Curve Sketching, Indeterminate Forms, L’Hopital’s Rule, Applied Optimization.

Chapter 5

Integration: Definite Integral, The Fundamental Theorem, Indefinite Integrals and the Substitution Method, Area Between Curves.

Chapter 1  Atomic and Molecular Structure                                      (12 Hrs)

Atomic Structure; Distribution of Electrons in Different Energy Levels; Valence Shell and Valence Electrons; Isotopes; Isobars; Nature of Light and Electromagnetic Waves; Wave Nature of Light; Electromagnetic Spectrum; Quantum Nature of Light; Photoelectric Effect; Bohr’s Theory of Atomic Structure; Drawbacks of Bohr Model; Quantum Mechanical Model of the Atom; Dual Nature of Electron (Wave Nature and Particles); Heisenberg’s Uncertainty Principle; Orbitals and Quantum Numbers; Quantum Number; Principle Quantum Number; Azimuthal Quantum Number; Magnetic Quantum Number; Spin Quantum Number; Pauli’s Exclusion Principle; Electronic Configuration of Atoms; Aufbau Principle; Hund’s Rule of Maximum Multiplicity; Writing Lewis Structures; Formal Charge; The Structure of Molecules; Some Terminology; Valence Shell Electron-Pair Repulsion (VSEPR ) Theory; Possibility for Electron Pair Distribution; Applying VSEPR Theory; Structures with Multiple Covalent Bonds; Molecular Shapes and Dipole moments.

Chapter 2  Principle of Chemical Equilibrium                                      (8 Hrs)

Dynamic Equilibrium; The Equilibrium Constant Expression; Relationships involving Equilibrium constants; Relationship of Kc to the Balanced Chemical Equation; Combining Equilibrium Constant Expression; Equilibria involving Gases: The Equilibrium Constant, Kp; Equilibria involving Liquids and Solids; The Reaction Quotient, Q; Predicting the Direction of a Net Reaction; Altering Equilibrium Conditions; Lechatelier’s Principle; Effect of Changes the Amounts of Reacting Species on Equilibrium; Effect of Changes in Pressure or Volume on Equilibrium; Effect of Temperature on Equilibrium; Effect of a Catalyst on Equilibrium; Equilibrium Calculation: Some Ilustrative Examples.

Chapter 3  Chemistry of Engineering Materials                                 (10 Hrs)

Refractories:   Characteristics of a good Refractory; Classification of Refractories; Manufacture of Refractories; Properties of Refractories; Important Refractories.

Abrasives:       Abrasive Power; Properties of Abrasives; Classification of Abrasives; Uses of Abrasives.

Adhesives:      Requirements of a Good Adhesive; Advantages of Adhesive Bonding; Disadvantages of Limitations of Adhesive Bonding; Development of Adhesive Strength; Classification of Adhesives.

Lubricants:      Functions of a Lubricant; Classification of Lubricants, Characteristics of Good Lubricants.

Ceramics:        Basic Raw Materials for Ceramics; General Properties of Ceramics; Manufacturing Process; Cement; Gypsum.

Composites:    Composites Material Structure; Types of Composites, Applications of Composites Materials.

Chapter 4  Metals and Their Applications                                              (10 Hrs)

Metallurgy ( Extracting a Metal from its Ore) - Common Ores, Isolation of Metals from its Ores; Zinc – Production of Zinc from Zinc Blend, Uses (Zn); Iron and Steel – Uses (Iron and Steel); Copper- Isolation and Electro Refining of Copper, Uses (Cu); Aluminium – Production of Aluminium, Properties and Uses of Aluminium; Silver – Properties and Uses of Silver.

Chapter 1

Complex Numbers: Complex Number &Plane, Polar Form of Complex Numbers powers &Roots.
Linear Algebra I

Chapter 2

Technique of integration: Integration by parts, Trigonometric Integrals, Trigonometric Substitution, Integration of  Rational Function by partial function, Improper integrals.

Chapter 3

Conic Section: Equations from the Distance Formula, Circle, Parabola, Ellipes, Hyperbola.

Chapter 4

Probability Theory: Experiment, Outcomes, Events, Probability.

Chapter 5

Permutation, Combination And Mathematical Induction: Permutation, Combination, Mathematical Induction.

Blueprint B1+ Upper Intermediate

Chapter 1

Applications of Definite Integrals, Volume Using Cross- Sections,Volumes Using Cylindrical shells, Arc Length, Areas of Surfaces of Revolution

Chapter 2

Integrals and Transcendental Functions: The logarithm Defined as an Integral, Hyperbolic Functions. 

Chapter 3

Parametric Equations and Polar Coordinates: Parameterizations of Curves , Plane Curves, Calculus with  Parametric Curves, Polar Coordinates, Area and Length in Polar  Coordinates

Chapter 4

Vectors and Geometry of Space: The Dot Products, The Cross Product,  Lines in Planes in Space, 

Chapter 5

Linear Algebra II: Vectors in Euclidean n Space, Matrices and Simultaneous Linear Equation, Eigenvalues, Eigenvectors.

Chapter 1

Vector Valued Function: Curves in space and their tangents, Integrals of  vector Function, Projectile motion, Arc Length in Space, Curvature and Normal Vector, Tangent  and Normal  Components of Acceleration, Velocity and Acceleration in Polar.

Chapter 2

Partial Differentiation: Limits and Continuity  in Higher Dimension: Partial derivatives, Chain rule, Directional derivatives and gradient vector, Tangent planes and differentials, Extreme values and Saddle points 

Chapter 3

Multiple Integrals: Double and iterated integrals over rectangular, Double integrals over general regions , Area by double integration, Double integrals in Polar form, Triple integral in rectangular coordinates  

Chapter 4

Vector Analysis: Line Integrals, Vector fields work circulation and flux, Path and independence, conservative field, Potential functions, Green’s Theorem, Surface and Area, Surface Integrals

Chapter 5

Infinite Series: Sequence , Infinite Series, The Integral Tests, Comparism Tests, The Ratio And Root Tests, Alternating Series, Absolute and Conditional Convergence , Revision

Blueprint B2 - Pre-Advanced 

Chapter 1
First order ODEs: Separable ODEs. Integrating Factors, Linear OGDs. Bernoulli Equation.

Chapter 2

Second –order Linear ODEs: Wronskian, Non-Homogeneous ODEs, Solution by Variation of Parameters

Chapter 3

Higher order linear ODEs: Homogeneous linear ODEs, Homogeneous linear ODEs with constant coefficients, Non-homogeneous linear ODEs

Chapter 4

Laplace Transforms: Laplace Transforms, Inverse Transform. Linearity.        s-Shifting, Transforms of Derivatives & Integrals ODEs, Unit Step Function. t- Shifting

Chapter 5

Fourier Series: Fourier Series, Functions of Any Period p=2L, Even & Odd Functions. Half- Range Expansions, Complex Fourier Series, Revision

Chapter 1
Complex  Analytic Function: Derivative Analytic Functions, Cauchy- Riemann Equations, Laplace Equations, Exponential Equations, Trigonometric and Hyperbolic Functions, Logarithm

Chapter 2

Complex Integration: Linear Integral In the Complex Planes, Cauchy’s Integral Theorem , Cauchy’s Integral Formula, Derivatives of Analytic Functions

Chapter 3

Power Series: Taylor Series: Laurent Series,Convergent Test, Power Series, Taylor and Maclaurin Series

Chapter 4

Integration by the Method of Residues : Laurent Series, Singularity Zeros, Infinity, Residues Integration methods

Chapter 5

Conformal: Geometry of Analytics Function: Linear Fractional Transformations, Special Linear transformations

Blueprint C1 - Advanced

Chapter 1
Numeric In General: Solution of Equations By Iteration, Interpolation, Numbers of Integration and Differentiation

Chapter 2

Numeric Linear Algebra: Linear System LU, Solution by Iteration, Least Square Methods. Inclusion of Matrices, Power Methods of Eigen Values, Tridiagonalization and QR Factorization

Chapter 4

Numeric for ODEs and PDEs: Methods for First Order, Multistep Methods, Methods for Higher Order

Chapter 5

Unconstrained optimization linear Programming : Basic Concepts, linear Programming , Simplex Methods

Chapter 1

Probability, Statistics + Queueing Theory: Random variable. Probability Distribution, Mean and Variance of a Distribution, Binomial, Poisson and Hypergeometric Distribution, Normal Distribution, Distribution  of Several Random Variables, Queueing Theory

Chapter 2

Mathematical Statistics: Confidence intervals

Chapter 3

Graphs: Combinatorial Optimization: Graphs and Digraphs, Shortest Path Problems, Bellman’s Principle, Shortest spanning Trees, Flow in Networks, Maximum flow, Bipartite Graphs, Revision