{"id":2193,"date":"2024-05-21T23:24:07","date_gmt":"2024-05-22T06:24:07","guid":{"rendered":"https:\/\/gantovnik.com\/bio-tips\/?p=2193"},"modified":"2024-05-25T00:40:32","modified_gmt":"2024-05-25T07:40:32","slug":"427-approximated-calculation-using-the-definition-of-derivative","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2024\/05\/427-approximated-calculation-using-the-definition-of-derivative\/","title":{"rendered":"#427 Approximated calculation using the definition of derivative"},"content":{"rendered":"pdf<\/a>\n

This is a small example which I prepared for my son to show him how to use the definition of derivative for approximate calculation.
\n\"\"<\/a>1<\/p>\n","protected":false},"excerpt":{"rendered":"

This is a small example which I prepared for my son to show him how to use the definition of derivative for approximate calculation. 1<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"yes","_lmt_disable":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[56],"tags":[],"class_list":["post-2193","post","type-post","status-publish","format-standard","hentry","category-math"],"modified_by":"gantovnik","jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8bH0k-zn","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":10721,"url":"https:\/\/gantovnik.com\/bio-tips\/2026\/01\/467-approximate-solution-of-a-boundary-value-problem-using-the-collocation-method-in-mathematica\/","url_meta":{"origin":2193,"position":0},"title":"#467 Approximate Solution of a Boundary Value Problem Using the Collocation Method in Mathematica","author":"gantovnik","date":"2026-01-10","format":false,"excerpt":"Mathematica source code: ClearAll[\"Global`*\"] yN = c1*(1 - x^2) + c2*x^2*(1 - x^2) D[yN[x], x] D[yN[x], {x, 2}] Clear[yN] yN[x_] := c1*(1 - x^2) + c2*x^2*(1 - x^2) yNp = yN'[x]; (*first derivative*) yNpp = yN''[x]; (*second derivative*) Simplify \/@ {yN[x], yNp, yNpp} L[x_] := yNpp + (1 + x^2)*yN[x]\u2026","rel":"","context":"In "differential equations"","block_context":{"text":"differential equations","link":"https:\/\/gantovnik.com\/bio-tips\/category\/differential-equations\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2026\/01\/ex467-1.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2026\/01\/ex467-1.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2026\/01\/ex467-1.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2026\/01\/ex467-1.png?resize=700%2C400&ssl=1 2x"},"classes":[]},{"id":648,"url":"https:\/\/gantovnik.com\/bio-tips\/2020\/09\/105-how-to-remove-offsets-defined-on-shell-and-beams\/","url_meta":{"origin":2193,"position":1},"title":"#105: How to remove offsets defined on shell and beams?","author":"gantovnik","date":"2020-09-25","format":false,"excerpt":"#105: How to remove offsets defined on shell and beams? Method 1: Properties > Modify > GLOBAL Method 2: Utility > Property > Property Editor Property Words to Change: 4111 Plate Offset, Only Process If Exists: Check, Action: =, Value: 0 Offsets should not be used for the beam and\u2026","rel":"","context":"In "nastran"","block_context":{"text":"nastran","link":"https:\/\/gantovnik.com\/bio-tips\/category\/nastran\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2146,"url":"https:\/\/gantovnik.com\/bio-tips\/2024\/04\/418-some-comments-about-exclude-command-in-linear-buckling-analysis-using-optistruct\/","url_meta":{"origin":2193,"position":2},"title":"#418 Some comments about EXCLUDE command in Linear Buckling Analysis using OptiStruct","author":"gantovnik","date":"2024-04-10","format":false,"excerpt":"The EXCLUDE command can be used to select a set of elements to be excluded from a Linear Buckling Analysis. EXCLUDE = ESID (ESID is Set identification number of an element set) The excluded elements are only removed from the geometric stiffness matrix, resulting in a Buckling Analysis with elastic\u2026","rel":"","context":"In "HyperMesh"","block_context":{"text":"HyperMesh","link":"https:\/\/gantovnik.com\/bio-tips\/category\/hypermesh\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":374,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/tkinter-pack-geometry-manager\/","url_meta":{"origin":2193,"position":3},"title":"#53 Tkinter pack geometry manager","author":"gantovnik","date":"2019-01-30","format":false,"excerpt":"","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example63","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example63.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1558,"url":"https:\/\/gantovnik.com\/bio-tips\/2022\/09\/210-parametric-curve-in-3d-2-2-2-2-2-2-2-2-2-2-2-2-2-3-3-2-2-3-2\/","url_meta":{"origin":2193,"position":4},"title":"#301 Buckling Glossary","author":"gantovnik","date":"2022-09-13","format":false,"excerpt":"Asymmetric buckling: When the structure has asymmetric geometry it may undergo stable buckling for a positive displacement parameter and unstable buckling if this displacement parameter is negative. Bifurcation point: A point along a primary equilibrium path (or curve) intersected by a secondary path. Beyond this point, the primary equilibrium path\u2026","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":508,"url":"https:\/\/gantovnik.com\/bio-tips\/2020\/05\/the-button-widget\/","url_meta":{"origin":2193,"position":5},"title":"#76 The Button widget","author":"gantovnik","date":"2020-05-06","format":false,"excerpt":"The Button widget","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2020\/05\/2020-05-06_012455.png?resize=350%2C200","width":350,"height":200},"classes":[]}],"_links":{"self":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/comments?post=2193"}],"version-history":[{"count":3,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2193\/revisions"}],"predecessor-version":[{"id":2198,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2193\/revisions\/2198"}],"wp:attachment":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media?parent=2193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/categories?post=2193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/tags?post=2193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}