Mathematics for scientific and technical students

Summary of contents

• Part 1 Algebra: quadratic equations
• equations reducible to quadratic form
• simultaneous equations
• indices
• logarithms
• the laws of logarithms
• changing the base of a logarithm
• solution of indicial equations
• tranposition of equations containing logarithms and indices
• partial fractions
• Part 2 Computation: rounding off numbers
• significant figures
• computational accuracy
• definition of error
• error prediction
• standard form
• Part 3 Trigonometry: trigometric ratios
• theorem of Pythagoras
• trigonometric ratios for 0, 30, 45, 60, 90
• trigonometric ratios of angles greater than 90
• the sine and cosine rules
• area of a triangle
• trigonometric graphs
• other trigonometric ratios
• trigonometric identities
• trigonometric ratios of compound angles
• double angle formulae
• sum and difference formulae
• trigonometric equations
• inverse trigonometric functions
• Part 4 Differentiation: functional notation
• incremental values
• limits
• the gradient of a curve
• differentiation
• differentiation of y=px, where p, n are constants
• another notation for the differential co-efficient
• differentiation of polynomials
• repeated differentiation
• differentiation of a function of a function
• differentiation of the product of two functions
• differentiation of a quotient of two functions
• the limit of sin 0/0 as 0 0, 0 being in radians
• the diffential co-efficient of the trigonometric functions
• differentiation of more difficult trigonometric functions
• differentiation of an implicit function
• to differentiate the exponential function
• to differentiate the log function
• examples of the differentiation of products and quotients of mixed functions
• differential equations
• the differentiation of the inverse trigonometric functions
• Part 5 Applications of differentiation: application to gradients of curves
• velocity of sound in a gas
• velocity and acceleration
• turning points
• practical examples of turning points
• rates of change with time
• partial differentiation
• application of partial differentiation to the estimation of error
• Part 6 Integration: the area between a curve and the x-axis
• integration - the method of obtainig the exact area under a curve
• the areas under simple curves
• integration of algebraic functions containing co-efficients
• area between a curve and the y-axis
• integration as the reverse of differentiation - the indefinite integral
• integration of more difficult algebraic functions
• further examples of areas under curves
• volumes of revolution
• volumes of a cone
• volumes of a sphere
• integration by substitution
• functions which integrate to give the logarithm function
• integration of the trigonometric functions
• integration of the trigonometric functions containing compound angles of the form (bx + c)
• integration of the squared trigonometric functions
• integration of the exponential function
• integration by partial fractions
• integration of a product of two functions (integration by parts)
• to determine lln x dx
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