MATHalino

Exponents and radicals • Logarithm and division by zero • Quadratic equation, quadratic formula, and roots of quadratic equation • Special products and factoring • Arithmetic, geometric, and harmonic progressions • Binomial expansion and Pascal's triangle • System of Equations • Variation and Proportion • Word Problems in Algebra • Number problems • Digit problems • Money/Coin problems • Geometry problems • Clock problems • Age problems • Mixture problems • Work problems • Motion problems
 

The six trigonometric functions • Trigonometric identities • Functions of a Right Triangle • Sum and difference of two angles • The spherical triangle • Right spherical triangle • Oblique spherical triangle
 

Triangle • Centers of a Triangle • Properties of Triangle • Quadrilateral • Common quadrilaterals • Cyclic quadrilateral • Tangential quadrilateral • Polygon • Regular polygon • Circle, sector of a circle, segment of a circle • Central angle and inscribed angle
 

Solids for which volume is the product of base area and altitude • Prism • Cube and rectangular parallelipiped • Cylinder • Right Circular Cylinder • Solids for which volume is one-third of the product of base area and altitude • Cone • Right circular cone • Pyramid • Regular pyramid • Regular tetrahedron • Frustum • Frustum of a Regular Pyramid • Frustum of a Right Circular Cone • Similar Figures • Sphere • Spherical sector • Spherical segment • Spherical wedge and spherical lune • Spherical zone • The Prismatoid and the Prismoidal Formula • Summary and Review
 

The Straight Line • The Circle • Parabola • Conic sections • Ellipse • Elements of Ellipse • Hyperbola • Equation of the Locus • Polar Coordinates
 

Fundamentals • Relation and Function • Theorems on Limits • The Derivative • Applications • Curvature and Radius of Curvature • Maxima and minima • Application of maxima and minima / Optimization problems • Time rates • Differentiation of trigonometric and inverse trigonometric functions • Optimization using trigonometric functions • Problems involving inverse trigonometric functions • Partial Differentiation
 

Indefinite Integrals • Properties of integrals • Definite integration • The General Power Formula • Logarithmic formula • Exponential formula • Integration of trigonometric functions • Integration of inverse trigonometric functions • Integration by parts • Integration by algebraic substitution • Integration by trigonometric substitution • Integration of rational fractions • Plane areas in rectangular coordinates • Plane areas in polar coordinates • Length of arc in rectangular plane • Length of arc in polar plane • Solids of revolution by integration
 

Components of planar and space forces • Moment • Couple • Resultant of concurrent forces • Resultant of parallel forces • Resultant of non-concurrent non-parallel forces • Equilibrium of concurrent forces • Equilibrium of parallel forces • Equilibrium of non-concurrent non parallel forces • Truss analysis • Method of joints • Method of sections • Simple frame analysis • Friction forces • Friction on wedges • Centroids and Centers of Gravity • Moment of Inertia and Radius of Gyration • Rectilinear Translation • Projectile Motion • Force Systems in Space
 

Normal Stress • Shear Stress • Bearing Stress • Thin-walled Pressure Vessels • Stress-strain Diagram • Axial Deformation • Shearing Deformation • Statically Indeterminate Members • Thermal Stress • Torsion • Flanged bolt couplings • Torsion of thin-walled tube • Helical Springs • Shear and Moment in Beams • Shear and Moment Diagrams • Relationship Between Load, Shear, and Moment • Load and moment diagrams for a given shear diagram • Moving Loads • Flexure Formula • Economic Sections • Floor Framing • Unsymmetrical Beams • Superimposed or Built-up Beams • Horizontal Shearing Stress • Design for Flexure and Shear • Spacing of Rivets or Bolts in Built-Up Beams • Beam Deflections • Double Integration Method • Moment Diagrams by Parts • Area-Moment Method • Deflection of Cantilever Beams • Deflections in Simply Supported Beams • Midspan Deflection • The Superposition Method • Castigliano’s Theorem • Conjugate Beam Method • Restrained Beams • Fixed-end moments • Continuous Beams • Three-Moment Equation • Reactions of Continuous Beams • Continuous Beams with Fixed Ends • Deflections by Three-Moment Equation • Moment Distribution Method • Combined Stresses • Combined Axial and Bending • Eccentrically Loaded Short Columns • Reinforced Beams • Transformed Section
 

Simple interest • Compound interest • Annuity • Ordinary annuity, annuity due, deffered annuity, and perpetuity
 

Derivation of Formulas • Elementary Differential Equations • Advance Engineering Mathematics • Surveying and Transportation Engineering • Structural Analysis • Fluid Mechanics and Hydraulics • Geotechnical Engineering • Timber Design • Reinforced Concrete Design
 

List of Greek alphabets and its English equivalent • Base Units in SI • Derived SI Units • Prefixes for SI Units • The English System of Units • Properties of common materials