College Algebra
Exponents and radicals • Logarithm and division by zero • Quadratic equation, quadratic formula, and roots of quadratic equation • Special products and factoring • Binomial expansion and Pascal's triangle • Verbal problem categories • Number problems • Digit problems • Clock problems • Age problems • Mixture problems • Work problems • Motion problems |
Plane and Spherical Trigonometry
The six trigonometric functions • Trigonometric identities • Sum and difference of two angles • The spherical triangle • Right spherical triangle • Oblique spherical triangle
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Plane Geometry
Triangle • Centers of a Triangle • Properties of Triangle • Quadrilateral • Cyclic quadrilateral • Polygon • Regular polygon • Circle, sector of a circle, segment of a circle |
Solid Mensuration / Solid Geometry
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 |
Analytic Geometry
Conic sections • Ellipse • Hyperbola • Parabola
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Differential Calculus
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 |
Integral Calculus
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 • Solids of revolution by integration |
Engineering Mechanics
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
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Strength of Materials / Mechanics of Materials
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 • Beam Deflection by Double Integration Method • Moment Diagrams by Parts • Beam Deflection by Area-Moment Method • Deflection of Cantilever Beams • Deflections in Simply Supported Beams • Beam Deflection by Method of Superposition • Restrained Beams Continuous Beams Combined Stresses Reinforced Beams |
Engineering Economy
Simple interest • Compound interest • Annuity • Ordinary annuity, annuity due, deffered annuity, and perpetuity
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Derivation of Formulas
Quadratic formula • Sum and product of roots of a quadratic equation • Arithmetic progression • Sum of finite and infinite geometric progression • Arithmetic mean, harmonic mean, and geometric mean •, Depreciation formula: SYD method • Proof of Ptolemy's theorem • Area of cyclic quadrilateral • Radius of circumcircle • Radius of incircle • Hero's formula for triangle of given three sides • Fundamental identities • Pythagorean identities • Cosine law • Pythagorean theorem • Sine law • Sum and difference of two angles • Double angle formulas • Half angle formulas • Volume of the frustum • Volume of sphere • Surface of the sphere • Lateral area of right circular cone |
Misccelanneous
List of Greek alphabets and its English equivalent • Meter, kilogram, second, and other base units in SI • Newton, Pascal, Watt, Coluomb and other derived SI units • SI unit prefixes from Yocto to Yotta • The English system of units
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