Minorsky V.P. Problems in higher mathematics

Moscow: Mir Publishers, 1975. — 396 p.The list of topics covered is quite exhaustive and the book has over 2500 problems and solutions. The topics covered are plane and solid analytic geometry, vector algebra, analysis, derivatives, integrals, series, differential equations etc. A good reference for those looking for many problems to solve.
The book was translated from the Russian by Yuri Ermolyev and was first published by Mir Publishers in 1975.Plane Analytic Geometry
Coordinates of a Point on· a Straight Line and in a Plane. The Distance Between Two Points
Dividing a Line Segment in a Given Ratio. The Area of a Triangle and a Polygon
The Equation of a Line as a Locus of Points
The Equation of a Straight Line: (1) Slope-Intercept Form, (2) General Form, (3) Intercept Form
The Angle Between Two Straight Lines. The Equation of a Pencil of Straight Lines Passing Through a Given Point. The Equation of a Straight Line Passing Through Two Given Points. The Point of Intersection of Two Straight Lines
The Normal Equation of a Straight Line. The Distance of a Point from a Straight Line. Equations of Bisectors. The Equations of a Pencil of Straight Lines Passing Through the Point of Intersection of Two Given Straight Lines
Miscellaneous Problems
The Circle
The Ellipse
The Hyperbola
The Parabola
Directrices, Diameters, and Tangents to Curves of the Second Order
Transformation of Cartesian Coordinates
Miscellaneous Problems on Second-Order Curves
General Equation of a Second-Order Curve
Polar Coordinates
Algebraic Curves of the Third and Higher Orders
Transcendental CurvesVector Algebra
Addition of Vectors. Multiplication of a Vector by a Scalar
Rectangular Coordinates of a Point and a Vector in Space
Scalar Product of Two Vectors
Vector Product of Two Vectors
Scalar Triple ProductSolid Analytic Geometry
The Equation of a Plane
Basic Problems Involving the Equation of a Plane
Equations of a Straight Line in Space
A Straight Line and a Plane
Spherical and Cylindrical Surfaces
Conical Surfaces and Surfaces of Revolution
The Ellipsoid, Hyperboloids, and ParaboloidsHigher Algebra
Determinants
Systems of First-Degree Equations
Complex Numbers
Higher-Degree Equations. Approximate Solution of EquationsIntroduction to Mathematical Analysis
Variable Quantities and Functions
Number Sequences. Infinitesimals and Infinities. The Limit of a Variable. The Limit of a Function
Basic Properties of Limits. Evaluating the Indeterminate Forms 0/0 \infty/ infty
The Limit of the Ratio sin(x)/x as x--> \infty
Indeterminate Expressions of the Form \infty --> \infty
Miscellaneous Problems on Limits
Comparison of Infinitesimals
The Continuity of a Function
Asymptotes
The NumberThe Derivative and the Differential
The Derivatives of Algebraic and Trigonometric Functions
The Derivative of a Composite Function
The Tangent Line and the Normal to a Plane Curve
Cases of Non-differentiability of a Continuous Function
The Derivatives of Logarithmic and Exponential Functions
The Derivatives of Inverse Trigonometric Functions
The Derivatives of Hyperbolic Functions
Miscellaneous Problems on Differentiation
Higher-Order Derivatives
The Derivative of an Implicit Function
The Differential of a Function
Parametric Equations of a CurveApplications of the Derivative
Velocity and Acceleration
Mean-Value Theorems
Evaluating Indeterminate Forms. L'Hospital's Rule
Increase and Decrease of a Function. MAXIMA and Minima
Finding Greatest and Least Values of a Function
Direction of Convexity and Points of Inflection of a Curve. Construction of GraphsThe Indefinite Integral
Indefinite Integral. Integration by Expansion
Integration by Substitution and Direct Integration
Integrals of the form dx and Those Reduced to Them
Integration by Parts
Integration of Some Trigonometric Functions
Integration of Rational Algebraic Functions
Integration of Certain Irrational Algebraic Functions
Integration of Certain Transcendental Functions
Integration of Hyperbolic Functions. Hyperbolic Substitutions
Miscellaneous Problems on IntegrationThe Definite Integral
Computing the Definite Integral
Computing Areas
The Volume of a Solid of Revolution
The Arc Length of a Plane Curve
The Area of a Surface of Revolution
Problems in Physics
ImproperIntegrals
The Mean Value of a Function
Trapezoid Rule and Simpson's FormulaCurvature of Plane and Space Curves
Curvature of a Plane Curve. The Centre and Radius of Curvature. The Evolute of a Plane Curve
The Arc Length of a Space Curve
The Derivative of a Vector Function of a Scalar Argument and Its Mechanical and Geometrical Interpretations. The Natural Trihedron of a Curve
Curvature and Torsion of a Space CurvePartial Derivatives, Total Differentials, and Their Applications
Functions of Two Variables and Their Geometrical Representation
Partial Derivatives of the First Order
Total Differential of the First Order
The Derivative of a Composite Function
Derivatives of Implicit Functions
Higher-Order Partial Derivatives and Total Differentials
Integration of Total Differentials
Singular Points of a Plane Curve
The Envelope of a Family of Plane Curves
The Tangent Plane and the Normal to a Surface
Scalar Field. Level Lines and Level Surfaces. A Derivative Along a Given Direction. Gradient
The Extremum of a Function of Two VariablesDifferential Equations
Fundamentals
First-Order Differential Equation with Variables Separable. Orthogonal Trajectories
First-Order Differential Equations: (I) Homogeneous, (2) Linear, (3) Bernoulli's
Differential Equations Containing Differentials of a Product or a Quotient
First-Order Differential Equations in Total Differentials. Integrating Factor
First-Order Differential Equations Not Solved for the Derivative. Lagrange's and Clairaut's Equations
Differential Equations of Higher Orders Allowing for Reduction of the Order
Linear Homogeneous Differential Equations with Cons- tant Coefficients
Linear Non-homogeneous Differential Equations with Constant Coefficients
Differential Equations of Various Types
Euler's Linear Differential Equation
Systems of Linear Differential Equations with Constant Coefficients
Partial Differential Equations of the Second Order (the Method of Characteristics)Double, Triple, and Line Integrals
Computing Areas by Means of Double Integrals
The Centre of Gravity and the Moment of Inertia of an Area with Uniformly Distributed Mass (for Density \mu = 1)
Computing Volumes by Means of Double Integrals
Areas of Curved Surfaces
The Triple Integral and Its Applications
The Line Integral. Green's Formula
Surface Integrals. Ostrogradsky's and Stokes' FormulasSeries
Numerical Series
Uniform Convergence of a Functional Series
Power Series
Taylor's and Maclaurin's Series
The Use of Series for Approximate Calculations
Taylor's Series for a Function of Two Variables
Fourier Series. Fourier IntegralAnswers
Appendices