--- title: Analytic Geometry description: Analytic geometry uses algebraic equations to represent and analyze geometric shapes on a coordinate plane. Learners will understand how to define lines, curves, and conic sections mathematically, bridging the gap between algebra and visual geometry. category: mathematics subcategory: geometry-and-trigonometry difficulty: beginner, intermediate, advanced url: /subject/analytic-geometry --- # Analytic Geometry Analytic geometry uses algebraic equations to represent and analyze geometric shapes on a coordinate plane. Learners will understand how to define lines, curves, and conic sections mathematically, bridging the gap between algebra and visual geometry. ## Available Resources 5 Books • 2 Courses • 1 Websites ## Courses ### 1. Multivariable Calculus (MIT 18.02SC) **Author:** Denis Auroux Differential, integral and vector calculus in several variables: vectors and matrices, partial derivatives, optimization, double and triple integrals, line integrals, and the theorems of Green, Stokes and Gauss. Includes 106 lecture and recitation videos, notes, and problems and exams with solutions, built for independent study. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/ **Tags:** multivariable-calculus, partial-derivatives, multiple-integrals, vector-calculus, line-integrals ### 2. Introducción al cálculo **Author:** Jaume Pujol, Mercè Villanueva Spanish-language course from the Universitat Autònoma de Barcelona that reviews numbers and functions, polynomial, exponential, logarithmic and trigonometric functions, then introduces differentiation, integration and complex numbers. Prepares students for a first-semester university calculus course in science or engineering. **Difficulty:** Beginner | **Language:** English | **Duration:** 6-8 horas de trabajo por módulo | **Price:** Free **Link:** https://www.coursera.org/learn/introduccion-al-calculo **Tags:** precalculus, functions, trigonometry, differentiation, integration, spanish-language ## Books ### 1. Geometry of Conics **Author:** A. V. Akopyan, A. A. Zaslavsky Compact monograph on the geometric properties of conics: optical and focal properties, pencils of conics, projective transformations, Poncelet's theorem, and related problems, combining synthetic, analytic, and projective methods with exercises. Advanced capstone for learners who have mastered coordinate conics and want their deeper structure. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0821843230?tag=edmonddante07-20 **Tags:** conic-sections, projective-geometry, poncelet-theorem, analytic-geometry, geometry ### 2. The Elements of Coordinate Geometry **Author:** S. L. Loney Classic Cartesian coordinate geometry text treating the straight line, circle, parabola, ellipse, hyperbola, polar equations, and the general second-degree equation, with large graded problem sets. Deepest free treatment of plane analytic geometry with thousands of exercises. Public-domain 1905 Macmillan edition, free to download. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://archive.org/details/elementsofcoordi00loneuoft **Tags:** analytic-geometry, coordinate-geometry, conic-sections, polar-coordinates, problem-sets ### 3. The Method of Coordinates **Author:** I. M. Gelfand, E. G. Glagoleva, A. A. Kirillov Unique conceptual primer on why coordinates work: short problem-driven text from Gelfand's Moscow correspondence school that builds coordinates from the number line up through the plane, space, and four dimensions, asking the reader to translate geometric questions into equations and inequalities. **Difficulty:** Beginner | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0486425657?tag=edmonddante07-20 **Tags:** analytic-geometry, coordinate-systems, cartesian-coordinates, problem-solving, higher-dimensions ### 4. Precalculus 2e, Chapter 10: Analytic Geometry **Author:** Jay Abramson et al. Best free on-ramp to conics as algebraic objects: free open textbook chapter covering the ellipse, hyperbola, and parabola in standard form, rotation of axes to remove the xy term, and conic sections in polar coordinates, with worked examples and graded exercise sets with answers. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://openstax.org/books/precalculus-2e/pages/10-introduction-to-analytic-geometry **Tags:** conic-sections, analytic-geometry, rotation-of-axes, polar-coordinates, precalculus ### 5. Analytic Geometry **Author:** Gordon Fuller, Dalton Tarwater Classic college textbook covering lines and circles, conic sections, simplification by translation and rotation of axes, polar and parametric equations, and three-dimensional coordinates with vectors, planes, and surfaces. Readers learn to move fluently between algebraic equations and their geometric curves. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0201134845?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, geometry--trigonometry ## Websites ### 1. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/analytic-geometry